A051912 -id:A051912 - cp's OEIS frontend

A093110 Numbers that can be written as a sum of three elements from A051912.

0, 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 15, 17, 18, 21, 26, 27, 30, 32, 33, 34, 36, 37, 39, 40, 45, 46, 49, 58, 64, 65, 68, 71, 72, 73, 75, 76, 77, 79, 84, 85, 88, 96, 97, 103, 104, 107, 116, 124, 125, 126, 128, 129, 132, 135, 137, 138, 141, 142, 143, 146, 150, 155, 156

Offset: 0

Wouter Meeussen, Mar 20 2004

a(n) increases as n^1.42.

			15 occurs since it can be written as 1 + 1 + 13; 16 does not occur since it cannot be written as a sum of at most 3 terms from the set {0,1,4,13,32,...} = A051912.

li=Take[A051912, 16]; Select[Union[Flatten[Outer[Plus, li, li, li]]], # <= Last[li] &]

A093111 Position of A051912 in A093110. a(n) is the number of integers < A051912(n) that can be expressed as a sum of three terms from A051912.

Original entry on oeis.org

0, 1, 4, 10, 19, 33, 49, 75, 110, 146, 181, 256, 312, 414, 486, 594, 710, 838, 948, 1184, 1300, 1522, 1758, 2042, 2279, 2546, 2754, 3148, 3411, 3856, 4179, 4611, 5043, 5560, 6213

Offset: 0

Wouter Meeussen, Mar 20 2004

a(n) increases as n^2.53

			a(3) = 10 since A051912(3)=13 and 13 =A093110(10), or there are 10 integers less than 13 that can be written as a sum of at most 3 terms from the set {0,1,4,13,32,..}=A051912.

Cf. A051912, A093110.

li=Take[A051912, 35]; Flatten[Position[A093110, # ]& / @ li]-1

A365515 Table read by antidiagonals upward: the n-th row gives the lexicographically earliest infinite B_n sequence starting from 0.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 0, 1, 3, 3, 0, 1, 4, 7, 4, 0, 1, 5, 13, 12, 5, 0, 1, 6, 21, 32, 20, 6, 0, 1, 7, 31, 55, 71, 30, 7, 0, 1, 8, 43, 108, 153, 124, 44, 8, 0, 1, 9, 57, 154, 366, 368, 218, 65, 9, 0, 1, 10, 73, 256, 668, 926, 856, 375, 80, 10, 0, 1, 11, 91, 333, 1153, 2214, 2286, 1424, 572, 96, 11

Offset: 1

Chai Wah Wu, Sep 07 2023

A B_n sequence is a sequence such that all sums a(x_1) + a(x_2) + ... + a(x_n) are distinct for 1 <= x_1 <= x_2 <= ... <= x_n. Analogous to A347570 except that here the B_n sequences start from a(1) = 0.

			Table begins:
n\k | 1  2   3   4    5     6      7      8       9
----+---------------------------------------------------
  1 | 0, 1,  2,  3,   4,    5,     6,     7,      8, ...
  2 | 0, 1,  3,  7,  12,   20,    30,    44,     65, ...
  3 | 0, 1,  4, 13,  32,   71,   124,   218,    375, ...
  4 | 0, 1,  5, 21,  55,  153,   368,   856,   1424, ...
  5 | 0, 1,  6, 31, 108,  366,   926,  2286,   5733, ...
  6 | 0, 1,  7, 43, 154,  668,  2214,  6876,  16864, ...
  7 | 0, 1,  8, 57, 256, 1153,  4181, 14180,  47381, ...
  8 | 0, 1,  9, 73, 333, 1822,  8043, 28296, 102042, ...
  9 | 0, 1, 10, 91, 500, 3119, 13818, 59174, 211135, ...

Chai Wah Wu, Table of n, a(n) for n = 1..242
Eric Weisstein's World of Mathematics, B2 Sequence.

Cf. A001477 (n=1), A025582 (n=2), A051912 (n=3), A365300 (n=4), A365301 (n=5), A365302 (n=6), A365303 (n=7), A365304 (n=8), A365305 (n=9), A002061 (k=4), A369817 (k=5), A369818 (k=6), A369819 (k=7), A347570.

from itertools import count, islice, combinations_with_replacement
def A365515_gen(): # generator of terms
    asets, alists, klist = [set()], [[]], [0]
    while True:
        for i in range(len(klist)-1,-1,-1):
            kstart, alist, aset = klist[i], alists[i], asets[i]
            for k in count(kstart):
                bset = set()
                for d in combinations_with_replacement(alist+[k],i):
                    if (m:=sum(d)+k) in aset:
                        break
                    bset.add(m)
                else:
                    yield k
                    alists[i].append(k)
                    klist[i] = k+1
                    asets[i].update(bset)
                    break
        klist.append(0)
        asets.append(set())
        alists.append([])
A365515_list = list(islice(A365515_gen(),30))

a(n) = A347570(n)-1.

A365300 a(n) is the smallest nonnegative integer such that the sum of any four ordered terms a(k), k<=n (repetitions allowed), is unique.

Original entry on oeis.org

0, 1, 5, 21, 55, 153, 368, 856, 1424, 2603, 4967, 8194, 13663, 22432, 28169, 47688, 65545, 96615, 146248, 202507, 266267, 364834, 450308, 585328, 773000, 986339, 1162748, 1472659, 1993180, 2275962, 3012656, 3552307, 4590959, 5404183, 6601787, 7893270, 9340877

Offset: 1

Kevin O'Bryant, Aug 31 2023

nonn

This is the greedy B_4 sequence.

			a(4) != 12 because 12+1+1+1 = 5+5+5+0.

Chai Wah Wu, Table of n, a(n) for n = 1..50
J. Cilleruelo and J Jimenez-Urroz, B_h[g] sequences, Mathematika (47) 2000, pp. 109-115.
Melvyn B. Nathanson, The third positive element in the greedy B_h-set, arXiv:2310.14426 [math.NT], 2023.
Melvyn B. Nathanson and Kevin O'Bryant, The fourth positive element in the greedy B_h-set, arXiv:2311.14021 [math.NT], 2023.
Kevin O'Bryant, A complete annotated bibliography of work related to Sidon sequences, Electron. J. Combin., DS11, Dynamic Surveys (2004), 39 pp.

Row 4 of A365515.

Cf. A025582, A051912, A365301, A365302, A365303, A365304, A365305.

def GreedyBh(h, seed, stopat):
    A = [set() for _ in range(h+1)]
    A[1] = set(seed)    # A[i] will hold the i-fold sumset
    for j in range(2,h+1): # {2,...,h}
        for x in A[1]:
            A[j].update([x+y for y in A[j-1]])
    w = max(A[1])+1
    while w <= stopat:
        wgood = True
        for k in range(1,h):
            if wgood:
                for j in range(k+1,h+1):
                    if wgood and (A[j].intersection([(j-k)*w + x for x in A[k]]) != set()):
                        wgood = False
        if wgood:
            A[1].add(w)
            for k in range(2,h+1): # update A[k]
                for j in range(1,k):
                    A[k].update([(k-j)*w + x for x in A[j]])
        w += 1
        return A[1]
GreedyBh(4,[0],10000)

from itertools import count, islice, combinations_with_replacement
def A365300_gen(): # generator of terms
    aset, alist = set(), []
    for k in count(0):
        bset = set()
        for d in combinations_with_replacement(alist+[k],3):
            if (m:=sum(d)+k) in aset:
                break
            bset.add(m)
        else:
            yield k
            alist.append(k)
            aset |= bset
A365300_list = list(islice(A365300_gen(),20)) # Chai Wah Wu, Sep 01 2023

a(27)-a(37) from Chai Wah Wu, Sep 01 2023

A036241 a(1)=1, a(2)=2, a(3)=3; for n >= 3, a(n) is smallest number such that all a(i) for 1 <= i <= n are distinct, all a(i)+a(j) for 1 <= i < j <= n are distinct and all a(i)+a(j)+a(k) for 1 <= i < j < k <= n are distinct.

Original entry on oeis.org

1, 2, 3, 5, 8, 14, 25, 45, 82, 140, 235, 388, 559, 839, 1286, 1582, 2221, 3144, 4071, 5795, 6872, 9204, 11524, 13796, 17686, 21489, 26019, 31080, 37742, 45067, 53144, 58365, 67917, 78484, 91767, 106513, 118600, 133486, 147633, 166034, 174717

Offset: 1

N. J. A. Sloane

			For {1,2,3,4} we have 1+4 = 2+3, so a(4) is not 4. For {1,2,3,5} the terms 1, 2, 3, 5 are distinct, the sums 1+2, 1+3, 1+5, 2+3, 2+5, 3+5 are distinct and the sums 1+2+3, 1+2+5, 1+3+5, 2+3+5 are distinct, so a(4) = 5.

Letter from V. Jooste, Pretoria, South Africa, Sep. 8, 1975.

Chai Wah Wu, Table of n, a(n) for n = 1..237 (n = 1..75 from Reinhard Zumkeller)

Cf. A011185, A062065, A051912, A060276.

import qualified Data.Set as Set (null, map)
import Data.Set (empty, fromList, toList, intersect, union)
a036241 n = a036241_list !! (n-1)
a036241_list = f [1..] [] empty empty where
   f (x:xs) ys s2 s3
    | null (s2' `intersect` y2s) && null (s3' `intersect` y3s)
      = x : f xs (x:ys) (fromList s2' `union` s2) (fromList s3' `union` s3)
    | otherwise = f xs ys s2 s3
    where s2' = sort $ map (x +) ys
          s3' = sort $ map (x +) y2s
          y2s = toList s2
          y3s = toList s3
-- Reinhard Zumkeller, Oct 02 2011

a[1]=1; a[2]=2; a[3]=3; a[n_] := a[n] = Catch[For[an = a[n-1] + 1, True, an++, a[n] = an; t2 = Flatten[Table[a[i] + a[j], {i, 1, n}, {j, i+1, n}]]; If[n*(n-1)/2 == Length[Union[t2]], t3 = Flatten[Table[a[i] + a[j] + a[k], {i, 1, n}, {j, i+1, n}, {k, j+1, n}]]; If[ n*(n-1)*(n-2)/6 == Length[Union[t3]], Throw[an]]]]]; Table[Print[a[n]]; a[n], {n, 1, 41}] (* Jean-François Alcover, Jul 24 2012 *)

{unique(v)=local(b); b=1; for(j=2,length(v),if(v[j-1]==v[j],b=0)); b}
{newsort(u,v,q)=local(s); s=[]; for(i=1,length(v),s=concat(s,v[i]+q)); vecsort(concat(u,s))}
{m=175000; print1(1,",",2,",",3,","); w1=[1,2,3]; w2=[3,4,5]; w3=[6]; q=4; while(q

from itertools import count, islice
def A036241_gen(): # generator of terms
    aset2, aset3 = {3,4,5}, {6}
    yield from (alist:=[1,2,3])
    for k in count(4):
        bset2, bset3 = set(), set()
        for a in alist:
            if (b2:=a+k) in aset2:
                break
            bset2.add(b2)
        else:
            for a2 in aset2:
                if (b3:=a2+k) in aset3:
                    break
                bset3.add(b3)
            else:
                yield k
                alist.append(k)
                aset2.update(bset2)
                aset3.update(bset3)
A036241_list = list(islice(A036241_gen(),20)) # Chai Wah Wu, Sep 10 2023

Better description and more terms from Naohiro Nomoto, Jul 02 2001

Edited by and terms a(30) to a(41) from Klaus Brockhaus, May 21 2003

A365301 a(n) is the smallest nonnegative integer such that the sum of any five ordered terms a(k), k<=n (repetitions allowed), is unique.

Original entry on oeis.org

0, 1, 6, 31, 108, 366, 926, 2286, 5733, 12905, 27316, 44676, 94545, 147031, 257637, 435387, 643320, 1107715, 1760092, 2563547, 3744446, 5582657, 8089160, 11373419, 15575157, 21480927, 28569028, 40893371, 53425354, 69774260, 93548428, 119627554

Offset: 1

Kevin O'Bryant, Aug 31 2023

This is the greedy B_5 sequence.

			a(4) != 20 because 20+1+1+1+1 = 6+6+6+6+0.

J. Cilleruelo and J Jimenez-Urroz, B_h[g] sequences, Mathematika (47) 2000, pp. 109-115.
Melvyn B. Nathanson, The third positive element in the greedy B_h-set, arXiv:2310.14426 [math.NT], 2023.
Melvyn B. Nathanson and Kevin O'Bryant, The fourth positive element in the greedy B_h-set, arXiv:2311.14021 [math.NT], 2023.
Kevin O'Bryant, A complete annotated bibliography of work related to Sidon sequences, Electron. J. Combin., DS11, Dynamic Surveys (2004), 39 pp.

Row 5 of A365515.

Cf. A025582, A051912, A365300, A365302, A365303, A365304, A365305.

def GreedyBh(h, seed, stopat):
    A = [set() for _ in range(h+1)]
    A[1] = set(seed)    # A[i] will hold the i-fold sumset
    for j in range(2,h+1): # {2,...,h}
        for x in A[1]:
            A[j].update([x+y for y in A[j-1]])
    w = max(A[1])+1
    while w <= stopat:
        wgood = True
        for k in range(1,h):
            if wgood:
                for j in range(k+1,h+1):
                    if wgood and (A[j].intersection([(j-k)*w + x for x in A[k]]) != set()):
                        wgood = False
        if wgood:
            A[1].add(w)
            for k in range(2,h+1): # update A[k]
                for j in range(1,k):
                    A[k].update([(k-j)*w + x for x in A[j]])
        w += 1
        return A[1]
GreedyBh(5,[0],10000)

from itertools import count, islice, combinations_with_replacement
def A365301_gen(): # generator of terms
    aset, alist = set(), []
    for k in count(0):
        bset = set()
        for d in combinations_with_replacement(alist+[k],4):
            if (m:=sum(d)+k) in aset:
                break
            bset.add(m)
        else:
            yield k
            alist.append(k)
            aset |= bset
A365301_list = list(islice(A365301_gen(),10)) # Chai Wah Wu, Sep 01 2023

a(18)-a(28) from Chai Wah Wu, Sep 01 2023
a(29)-a(30) from Chai Wah Wu, Sep 10 2023
a(31)-a(32) from Chai Wah Wu, Mar 02 2024

A365302 a(n) is the smallest nonnegative integer such that the sum of any six ordered terms a(k), k<=n (repetitions allowed), is unique.

Original entry on oeis.org

0, 1, 7, 43, 154, 668, 2214, 6876, 16864, 41970, 94710, 202027, 429733, 889207, 1549511, 3238700, 5053317, 8502061, 15583775, 25070899, 40588284, 63604514

Offset: 1

Kevin O'Bryant, Aug 31 2023

This is the greedy B_6 sequence.

			a(5) != 50 because 50+1+1+1+1+0 = 43+7+1+1+1+1.

J. Cilleruelo and J Jimenez-Urroz, B_h[g] sequences, Mathematika (47) 2000, pp. 109-115.
Melvyn B. Nathanson, The third positive element in the greedy B_h-set, arXiv:2310.14426 [math.NT], 2023.
Melvyn B. Nathanson and Kevin O'Bryant, The fourth positive element in the greedy B_h-set, arXiv:2311.14021 [math.NT], 2023.
Kevin O'Bryant, A complete annotated bibliography of work related to Sidon sequences, Electron. J. Combin., DS11, Dynamic Surveys (2004), 39 pp.

Row 6 of A365515.

Cf. A025582, A051912, A365300, A365301, A365303, A365304, A365305.

def GreedyBh(h, seed, stopat):
    A = [set() for _ in range(h+1)]
    A[1] = set(seed)    # A[i] will hold the i-fold sumset
    for j in range(2,h+1): # {2,...,h}
        for x in A[1]:
            A[j].update([x+y for y in A[j-1]])
    w = max(A[1])+1
    while w <= stopat:
        wgood = True
        for k in range(1,h):
            if wgood:
                for j in range(k+1,h+1):
                    if wgood and (A[j].intersection([(j-k)*w + x for x in A[k]]) != set()):
                        wgood = False
        if wgood:
            A[1].add(w)
            for k in range(2,h+1): # update A[k]
                for j in range(1,k):
                    A[k].update([(k-j)*w + x for x in A[j]])
        w += 1
        return A[1]
GreedyBh(6,[0],10000)

from itertools import count, islice, combinations_with_replacement
def A365302_gen(): # generator of terms
    aset, alist = set(), []
    for k in count(0):
        bset = set()
        for d in combinations_with_replacement(alist+[k],5):
            if (m:=sum(d)+k) in aset:
                break
            bset.add(m)
        else:
            yield k
            alist.append(k)
            aset |= bset
A365302_list = list(islice(A365302_gen(),10)) # Chai Wah Wu, Sep 01 2023

a(15)-a(19) from Chai Wah Wu, Sep 01 2023

a(20)-a(22) from Chai Wah Wu, Sep 09 2023

A365303 a(n) is the smallest nonnegative integer such that the sum of any seven ordered terms a(k), k<=n (repetitions allowed), is unique.

Original entry on oeis.org

0, 1, 8, 57, 256, 1153, 4181, 14180, 47381, 115267, 307214, 737909, 1682367, 3850940, 8557010, 18311575, 37925058, 61662056

Offset: 1

Kevin O'Bryant, Aug 31 2023

This is the greedy B_7 sequence.

			a(3) != 7 because 7+0+0+0+0+0+0 = 1+1+1+1+1+1+1.

J. Cilleruelo and J Jimenez-Urroz, B_h[g] sequences, Mathematika (47) 2000, pp. 109-115.
Melvyn B. Nathanson, The third positive element in the greedy B_h-set, arXiv:2310.14426 [math.NT], 2023.
Melvyn B. Nathanson and Kevin O'Bryant, The fourth positive element in the greedy B_h-set, arXiv:2311.14021 [math.NT], 2023.
Kevin O'Bryant, A complete annotated bibliography of work related to Sidon sequences, Electron. J. Combin., DS11, Dynamic Surveys (2004), 39 pp.

Row 7 of A365515.

Cf. A025582, A051912, A365300, A365301, A365302, A365304, A365305.

def GreedyBh(h, seed, stopat):
    A = [set() for _ in range(h+1)]
    A[1] = set(seed)    # A[i] will hold the i-fold sumset
    for j in range(2,h+1): # {2,...,h}
        for x in A[1]:
            A[j].update([x+y for y in A[j-1]])
    w = max(A[1])+1
    while w <= stopat:
        wgood = True
        for k in range(1,h):
            if wgood:
                for j in range(k+1,h+1):
                    if wgood and (A[j].intersection([(j-k)*w + x for x in A[k]]) != set()):
                        wgood = False
        if wgood:
            A[1].add(w)
            for k in range(2,h+1): # update A[k]
                for j in range(1,k):
                    A[k].update([(k-j)*w + x for x in A[j]])
        w += 1
        return A[1]
GreedyBh(7,[0],10000)

from itertools import count, islice, combinations_with_replacement
def A365303_gen(): # generator of terms
    aset, alist = set(), []
    for k in count(0):
        bset = set()
        for d in combinations_with_replacement(alist+[k],6):
            if (m:=sum(d)+k) in aset:
                break
            bset.add(m)
        else:
            yield k
            alist.append(k)
            aset |= bset
A365303_list = list(islice(A365303_gen(),10)) # Chai Wah Wu, Sep 01 2023

a(13)-a(18) from Chai Wah Wu, Sep 13 2023

A365304 a(n) is the smallest nonnegative integer such that the sum of any eight ordered terms a(k), k<=n (repetitions allowed), is unique.

Original entry on oeis.org

0, 1, 9, 73, 333, 1822, 8043, 28296, 102042, 338447, 1054824, 2569353, 6237718, 15947108, 36179796

Offset: 1

Kevin O'Bryant, Aug 31 2023

This is the greedy B_8 sequence.

			a(4) != 70 because 70+1+1+0+0+0+0+0 = 9+9+9+9+9+9+9+0.

J. Cilleruelo and J Jimenez-Urroz, B_h[g] sequences, Mathematika (47) 2000, pp. 109-115.
Melvyn B. Nathanson and Kevin O'Bryant, The fourth positive element in the greedy B_h-set, arXiv:2311.14021 [math.NT], 2023.
Kevin O'Bryant, A complete annotated bibliography of work related to Sidon sequences, Electron. J. Combin., DS11, Dynamic Surveys (2004), 39 pp.

Row 8 of A365515.

Cf. A025582, A051912, A365300, A365301, A365302, A365303, A365305.

def GreedyBh(h, seed, stopat):
    A = [set() for _ in range(h+1)]
    A[1] = set(seed)    # A[i] will hold the i-fold sumset
    for j in range(2,h+1): # {2,...,h}
        for x in A[1]:
            A[j].update([x+y for y in A[j-1]])
    w = max(A[1])+1
    while w <= stopat:
        wgood = True
        for k in range(1,h):
            if wgood:
                for j in range(k+1,h+1):
                    if wgood and (A[j].intersection([(j-k)*w + x for x in A[k]]) != set()):
                        wgood = False
        if wgood:
            A[1].add(w)
            for k in range(2,h+1): # update A[k]
                for j in range(1,k):
                    A[k].update([(k-j)*w + x for x in A[j]])
        w += 1
        return A[1]
GreedyBh(8,[0],10000)

from itertools import count, islice, combinations_with_replacement
def A365304_gen(): # generator of terms
    aset, alist = set(), []
    for k in count(0):
        bset = set()
        for d in combinations_with_replacement(alist+[k],7):
            if (m:=sum(d)+k) in aset:
                break
            bset.add(m)
        else:
            yield k
            alist.append(k)
            aset |= bset
A365304_list = list(islice(A365304_gen(),10)) # Chai Wah Wu, Sep 01 2023

a(11)-a(15) from Chai Wah Wu, Sep 13 2023

A365305 a(n) is the smallest nonnegative integer such that the sum of any nine ordered terms a(k), k<=n (repetitions allowed), is unique.

Original entry on oeis.org

0, 1, 10, 91, 500, 3119, 13818, 59174, 211135, 742330, 2464208, 7616100, 19241477, 56562573

Offset: 1

Kevin O'Bryant, Aug 31 2023

This is the greedy B_9 sequence.

			a(4) != 72 because 72+1+1+1+1+1+1+1+1+0 = 10+10+10+10+10+10+10+10+0.

J. Cilleruelo and J. Jimenez-Urroz, B_h[g] sequences, Mathematika (47) 2000, pp. 109-115.
Melvyn B. Nathanson, The third positive element in the greedy B_h-set, arXiv:2310.14426 [math.NT], 2023.
Melvyn B. Nathanson and Kevin O'Bryant, The fourth positive element in the greedy B_h-set, arXiv:2311.14021 [math.NT], 2023.
Kevin O'Bryant, A complete annotated bibliography of work related to Sidon sequences, Electron. J. Combin., DS11, Dynamic Surveys (2004), 39 pp.

Row 9 of A365515.

Cf. A025582, A051912, A365300, A365301, A365302, A365303, A365304.

def GreedyBh(h, seed, stopat):
    A = [set() for _ in range(h+1)]
    A[1] = set(seed)    # A[i] will hold the i-fold sumset
    for j in range(2,h+1): # {2,...,h}
        for x in A[1]:
            A[j].update([x+y for y in A[j-1]])
    w = max(A[1])+1
    while w <= stopat:
        wgood = True
        for k in range(1,h):
            if wgood:
                for j in range(k+1,h+1):
                    if wgood and (A[j].intersection([(j-k)*w + x for x in A[k]]) != set()):
                        wgood = False
        if wgood:
            A[1].add(w)
            for k in range(2,h+1): # update A[k]
                for j in range(1,k):
                    A[k].update([(k-j)*w + x for x in A[j]])
        w += 1
        return A[1]
GreedyBh(9,[0],10000)

from itertools import count, islice, combinations_with_replacement
def A365305_gen(): # generator of terms
    aset, alist = set(), []
    for k in count(0):
        bset = set()
        for d in combinations_with_replacement(alist+[k],8):
            if (m:=sum(d)+k) in aset:
                break
            bset.add(m)
        else:
            yield k
            alist.append(k)
            aset |= bset
A365305_list = list(islice(A365305_gen(),10)) # Chai Wah Wu, Sep 01 2023

a(11)-a(14) from Chai Wah Wu, Sep 13 2023

cp's OEIS Frontend

A093110 Numbers that can be written as a sum of three elements from A051912.

Views

Author

Keywords

Comments

Examples

Programs

Mathematica

A093111 Position of A051912 in A093110. a(n) is the number of integers < A051912(n) that can be expressed as a sum of three terms from A051912.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A365515 Table read by antidiagonals upward: the n-th row gives the lexicographically earliest infinite B_n sequence starting from 0.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

Formula

A365300 a(n) is the smallest nonnegative integer such that the sum of any four ordered terms a(k), k<=n (repetitions allowed), is unique.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

Python

Extensions

A036241 a(1)=1, a(2)=2, a(3)=3; for n >= 3, a(n) is smallest number such that all a(i) for 1 <= i <= n are distinct, all a(i)+a(j) for 1 <= i < j <= n are distinct and all a(i)+a(j)+a(k) for 1 <= i < j < k <= n are distinct.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Python

Extensions

A365301 a(n) is the smallest nonnegative integer such that the sum of any five ordered terms a(k), k<=n (repetitions allowed), is unique.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

Python

Extensions

A365302 a(n) is the smallest nonnegative integer such that the sum of any six ordered terms a(k), k<=n (repetitions allowed), is unique.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

Python

Extensions

A365303 a(n) is the smallest nonnegative integer such that the sum of any seven ordered terms a(k), k<=n (repetitions allowed), is unique.