A254100 -id:A254100 - cp's OEIS frontend

A256487 a(n) = A254100(n) - A219178(n).

2, 4, 0, 4, 10, 18, 16, 36, 28, 48, 78, 80, 62, 90, 76, 110, 134, 158, 200, 220, 224, 216, 236, 280, 308, 312, 262, 314, 328, 402, 430, 424, 438, 488, 506, 538, 414, 510, 642, 620, 680, 648, 656, 690, 666, 684, 730, 790, 742, 840, 844, 862, 916, 976, 1004, 1092, 1072, 1112, 1054, 1166, 1176, 1184, 1292

Offset: 1

Antti Karttunen, May 01 2015

nonn

Difference between the least nonludic number removed at the n-th stage of Ludic sieve and the least unlucky number removed at the n-th stage of Lucky sieve.

Antti Karttunen, Table of n, a(n) for n = 1..933
Index entries for sequences generated by sieves

Cf. A219178, A254100, A256482, A256486, A256488 (same terms divided by 2).

(define (A256487 n) (- (A254100 n) (A219178 n)))

a(n) = A254100(n) - A219178(n).

A256482 a(n) = A254100(n) - A003309(n+1).

Original entry on oeis.org

2, 6, 14, 24, 44, 60, 84, 122, 142, 176, 216, 252, 274, 308, 360, 412, 454, 498, 546, 594, 648, 672, 736, 810, 868, 908, 930, 994, 1040, 1130, 1188, 1254, 1310, 1398, 1444, 1484, 1500, 1614, 1748, 1780, 1866, 1890, 1944, 2012, 2040, 2096, 2154, 2240, 2328, 2436, 2488, 2544, 2676, 2740, 2800, 2948, 2976, 3034, 3090, 3210

Offset: 1

Antti Karttunen, Apr 30 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4096

Column 1 of A257257.
Cf. A003309, A254100.
Cf. also A256483 (same terms divided by 2).

(define (A256482 n) (- (A254100 n) (A003309 (+ 1 n))))

a(n) = A254100(n) - A003309(n+1).

a(n) = 2*A256483(n).

A276606 First differences of postludic numbers: a(n) = A254100(1+n) - A254100(n).

Original entry on oeis.org

5, 10, 12, 24, 18, 28, 44, 22, 38, 48, 40, 24, 38, 58, 60, 48, 48, 54, 54, 60, 26, 70, 84, 66, 44, 24, 70, 50, 102, 64, 74, 60, 100, 48, 44, 18, 126, 150, 34, 96, 26, 58, 74, 30, 60, 66, 96, 96, 120, 58, 60, 146, 70, 66, 164, 30, 64, 60, 132, 50, 40, 168, 78, 62, 100, 108, 104, 42, 58, 98, 40, 50, 100, 198, 44, 88, 60, 138, 60

Offset: 1

Antti Karttunen, Sep 13 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences generated by sieves

Column 2 of A276610.

Cf. also A260723, A276607.

(define (A276606 n) (- (A254100 (+ 1 n)) (A254100 n)))

a(n) = A254100(1+n) - A254100(n).

a(n) = A260723(1+n) + A276607(n).

A256483 a(n) = A256482(n)/2 = (A254100(n) - A003309(n+1)) / 2.

Original entry on oeis.org

1, 3, 7, 12, 22, 30, 42, 61, 71, 88, 108, 126, 137, 154, 180, 206, 227, 249, 273, 297, 324, 336, 368, 405, 434, 454, 465, 497, 520, 565, 594, 627, 655, 699, 722, 742, 750, 807, 874, 890, 933, 945, 972, 1006, 1020, 1048, 1077, 1120, 1164, 1218, 1244, 1272, 1338, 1370, 1400, 1474, 1488, 1517, 1545, 1605, 1627

Offset: 1

Antti Karttunen, May 01 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4096

Column 1 of A257258.
Cf. A003309, A254100, A256482.
Cf. also A256486, A256487.

Scheme
```
(define (A256483 n) (/ (A256482 n) 2))
```

a(n) = A256482(n)/2 = (A254100(n) - A003309(n+1)) / 2.

A256488 a(n) = A256487(n)/2 = (A254100(n) - A219178(n))/2.

Original entry on oeis.org

1, 2, 0, 2, 5, 9, 8, 18, 14, 24, 39, 40, 31, 45, 38, 55, 67, 79, 100, 110, 112, 108, 118, 140, 154, 156, 131, 157, 164, 201, 215, 212, 219, 244, 253, 269, 207, 255, 321, 310, 340, 324, 328, 345, 333, 342, 365, 395, 371, 420, 422, 431, 458, 488, 502, 546, 536, 556, 527, 583, 588, 592, 646, 643, 639, 665, 688, 662, 662

Offset: 1

Antti Karttunen, May 01 2015

nonn

Half the difference between the least nonludic number removed at the n-th stage of Ludic sieve and the least unlucky number removed at the n-th stage of Lucky sieve.

Antti Karttunen, Table of n, a(n) for n = 1..933

Cf. A219178, A254100, A256482, A256486, A256487.

Scheme
```
(define (A256488 n) (/ (A256487 n) 2))
```

a(n) = A256487(n)/2 = (A254100(n) - A219178(n))/2.

A276576 Column 2 of A276580: a(n) = A276570(A254100(n)); the n-th postludic number modulo the corresponding Ludic number.

Original entry on oeis.org

0, 0, 4, 3, 0, 8, 16, 7, 17, 2, 31, 6, 16, 26, 42, 46, 52, 1, 7, 13, 25, 35, 57, 61, 63, 75, 83, 105, 123, 129, 145, 155, 22, 14, 44, 52, 52, 70, 76, 92, 98, 106, 128, 148, 160, 184, 178, 184, 208, 220, 224, 248, 268, 284, 296, 316, 328, 1, 21, 33, 23, 43, 51, 69, 71, 91, 99, 123, 125, 163, 161, 181, 191, 211, 229, 233, 241, 241

Offset: 1

Antti Karttunen, Sep 13 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4098
Index entries for sequences generated by sieves

Cf. A003309, A254100, A276570.

Column 2 of A276580.

(define (A276576 n) (A276570 (A254100 n)))
;; Which reduces to:
(define (A276576 n) (modulo (A254100 n) (A003309 (+ 1 n))))

a(n) = A276570(A254100(n)) = A254100(n) modulo A003309(1+n).

A003309 Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th remaining number.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 17, 23, 25, 29, 37, 41, 43, 47, 53, 61, 67, 71, 77, 83, 89, 91, 97, 107, 115, 119, 121, 127, 131, 143, 149, 157, 161, 173, 175, 179, 181, 193, 209, 211, 221, 223, 227, 233, 235, 239, 247, 257, 265, 277, 283, 287, 301, 307, 313

Offset: 1

N. J. A. Sloane

The definition can obviously only be applied from k = a(2) = 2 on: for k = 1, all remaining numbers would be deleted. - M. F. Hasler, Nov 02 2024

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Donovan Johnson, Table of n, a(n) for n = 1..100000
David Applegate, C program for A003309.
Donovan Johnson, Ludic numbers computed up to A003309(1236290) = 23000711.
OEIS Wiki, Ludic numbers.
Popular Computing (Calabasas, CA), Sieves: Problem 43, Vol. 2 (No. 13, Apr 1974), pp. 6-7. This is Sieve #1. [Annotated and scanned copy]
Rosettacode Wiki, Ludic numbers.
Index entries for sequences generated by sieves

Without the initial 1 occurs as the leftmost column in arrays A255127 and A260717.
Cf. A003310, A003311, A100464, A100585, A100586 (variants).
Cf. A192503 (primes in sequence), A192504 (nonprimes), A192512 (number of terms <= n).
Cf. A192490 (characteristic function).
Cf. A192607 (complement).
Cf. A260723 (first differences).
Cf. A255420 (iterates of f(n) = A003309(n+1) starting from n=1).
Subsequence of A302036.
Cf. A237056, A237126, A237427, A235491, A255407, A255408, A255421, A255422, A260435, A260436, A260741, A260742 (permutations constructed from Ludic numbers).
Cf. also A000959, A008578, A255324, A254100, A272565 (Ludic factor of n), A297158, A302032, A302038.
Cf. A376237 (ludic factorial: cumulative product), A376236 (ludic Fortunate numbers).

a003309 n = a003309_list !! (n - 1)
a003309_list = 1 : f [2..] :: [Int]
   where f (x:xs) = x : f (map snd [(u, v) | (u, v) <- zip [1..] xs,
                                             mod u x > 0])
-- Reinhard Zumkeller, Feb 10 2014, Jul 03 2011

ludic:= proc(N) local i, k,S,R;
  S:= {$2..N};
  R:= 1;
  while nops(S) > 0 do
    k:= S[1];
    R:= R,k;
    S:= subsop(seq(1+k*j=NULL, j=0..floor((nops(S)-1)/k)),S);
  od:
[R];
end proc:
ludic(1000); # Robert Israel, Feb 23 2015

t = Range[2, 400]; r = {1}; While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}];]; r (* Ray Chandler, Dec 02 2004 *)

t=vector(399,x,x+1); r=[1]; while(length(t)>0, k=t[1];r=concat(r,[k]);t=vector((length(t)*(k-1))\k,x,t[(x*k+k-2)\(k-1)])); r \\ Phil Carmody, Feb 07 2007

A3309=[1]; next_A003309(n)=nn && break); n+!if(n=setsearch(A3309,n+1,1),return(A3309[n])) \\ Should be made more efficient if n >> max(A3309). - M. F. Hasler, Nov 02 2024
{A003309(n) = while(n>#A3309, next_A003309(A3309[#A3309])); A3309[n]} \\ Should be made more efficient in case n >> #A3309. - M. F. Hasler, Nov 03 2024

upto(nn)= my(r=List([1..nn]), p=1); while(p++<#r, my(k=r[p], i=p); while((i+=k)<=#r, listpop(~r, i); i--)); Vec(r); \\ Ruud H.G. van Tol, Dec 13 2024

remainders = [0]
ludics = [2]
N_MAX = 313
for i in range(3, N_MAX) :
    ludic_index = 0
    while ludic_index < len(ludics) :
        ludic = ludics[ludic_index]
        remainder = remainders[ludic_index]
        remainders[ludic_index] = (remainder + 1) % ludic
        if remainders[ludic_index] == 0 :
            break
        ludic_index += 1
    if ludic_index == len(ludics) :
        remainders.append(0)
        ludics.append(i)
ludics = [1] + ludics
print(ludics)
# Alexandre Herrera, Aug 10 2023

def A003309(): # generator of the infinite list of ludic numbers
    L = [2, 3]; yield 1; yield 2; yield 3
    while k := len(L)//2: # could take min{k | k >= L[-1-k]-1}
        for j in L[-1-k::-1]: k += 1 + k//(j-1)
        L.append(k+2); yield k+2
A003309_upto = lambda N=99: [t for t,_ in zip(A003309(),range(N))]
# M. F. Hasler, Nov 02 2024

(define (A003309 n) (if (= 1 n) n (A255127bi (- n 1) 1))) ;; Code for A255127bi given in A255127.
;; Antti Karttunen, Feb 23 2015

Complement of A192607; A192490(a(n)) = 1. - Reinhard Zumkeller, Jul 05 2011
From Antti Karttunen, Feb 23 2015: (Start)
a(n) = A255407(A008578(n)).
a(n) = A008578(n) + A255324(n).
(End)

More terms from David Applegate and N. J. A. Sloane, Nov 23 2004

A255127 Ludic array: square array A(row,col), where row n lists the numbers removed at stage n in the sieve which produces Ludic numbers. Array is read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Original entry on oeis.org

2, 4, 3, 6, 9, 5, 8, 15, 19, 7, 10, 21, 35, 31, 11, 12, 27, 49, 59, 55, 13, 14, 33, 65, 85, 103, 73, 17, 16, 39, 79, 113, 151, 133, 101, 23, 18, 45, 95, 137, 203, 197, 187, 145, 25, 20, 51, 109, 163, 251, 263, 281, 271, 167, 29, 22, 57, 125, 191, 299, 325, 367, 403, 311, 205, 37, 24, 63, 139, 217, 343, 385, 461, 523, 457, 371, 253, 41

Offset: 2

Antti Karttunen, Feb 22 2015

The starting offset of the sequence giving the terms of square array is 2. However, we can tacitly assume that a(1) = 1 when the sequence is used as a permutation of natural numbers. However, term 1 itself is out of the array.

The choice of offset = 2 for the terms starting in rows >= 1 is motivated by the desire to have a permutation of the integers n -> a(n) with a(n) = A(A002260(n-1), A004736(n-1)) for n > 1 and a(1) := 1. However, since this sequence is declared as a "table", offset = 2 would mean that the first *row* (not element) has index 2. I think the sequence should have offset = 1 and the permutation of the integers would be n -> a(n-1) with a(0) := 1 (if a(1) = A(1,1) = 2). Or, the sequence could have offset 0, with an additional row 0 of length 1 with the only element a(0) = A(0,1) = 1, the permutation still being n -> a(n-1) if a(n=0, 1, 2, ...) = (1, 2, 4, ...). This would be in line with considering 1 as the first ludic number, and A(n, 1) = A003309(n+1) for n >= 0. - M. F. Hasler, Nov 12 2024

			The top left corner of the array:
   2,   4,   6,   8,  10,  12,   14,   16,   18,   20,   22,   24,   26
   3,   9,  15,  21,  27,  33,   39,   45,   51,   57,   63,   69,   75
   5,  19,  35,  49,  65,  79,   95,  109,  125,  139,  155,  169,  185
   7,  31,  59,  85, 113, 137,  163,  191,  217,  241,  269,  295,  323
  11,  55, 103, 151, 203, 251,  299,  343,  391,  443,  491,  539,  587
  13,  73, 133, 197, 263, 325,  385,  449,  511,  571,  641,  701,  761
  17, 101, 187, 281, 367, 461,  547,  629,  721,  809,  901,  989, 1079
  23, 145, 271, 403, 523, 655,  781,  911, 1037, 1157, 1289, 1417, 1543
  25, 167, 311, 457, 599, 745,  883, 1033, 1181, 1321, 1469, 1615, 1753
  29, 205, 371, 551, 719, 895, 1073, 1243, 1421, 1591, 1771, 1945, 2117
...

Antti Karttunen, Table of n, a(n) for n = 2..10441; the first 144 antidiagonals of array, flattened

Transpose: A255129.
Inverse: A255128. (When considered as a permutation of natural numbers with a(1) = 1).
Cf. A260738 (index of the row where n occurs), A260739 (of the column).
Main diagonal: A255410.
Column 1: A003309 (without the initial 1). Column 2: A254100.
Row 1: A005843, Row 2: A016945, Row 3: A255413, Row 4: A255414, Row 5: A255415, Row 6: A255416, Row 7: A255417, Row 8: A255418, Row 9: A255419.
A192607 gives all the numbers right of the leftmost column, and A192506 gives the composites among them.
Cf. A272565, A271419, A271420 and permutations A269379, A269380, A269384.
Cf. also related or derived arrays A260717, A257257, A257258 (first differences of rows), A276610 (of columns), A276580.
Analogous arrays for other sieves: A083221, A255551, A255543.
Cf. A376237 (ludic factorials), A377469 (ludic analog of A005867).

rows = 12; cols = 12; t = Range[2, 3000]; r = {1}; n = 1; While[n <= rows, k = First[t]; AppendTo[r, k]; t0 = t; t = Drop[t, {1, -1, k}]; ro[n++] = Complement[t0, t][[1 ;; cols]]]; A = Array[ro, rows]; Table[ A[[n - k + 1, k]], {n, 1, rows}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Mar 14 2016, after Ray Chandler *)

a255127 = lambda n: A255127(A002260(k-1), A004736(k-1))
def A255127(n, k):
    A = A255127; R = A.rows
    while len(R) <= n or len(R[n]) < min(k, A.P[n]): A255127_extend(2*n)
    return R[n][(k-1) % A.P[n]] + (k-1)//A.P[n] * A.S[n]
A=A255127; A.rows=[[1],[2],[3]]; A.P=[1]*3; A.S=[0,2,6]; A.limit=30
def A255127_extend(rMax=9, A=A255127):
    A.limit *= 2; L = [x+5-x%2 for x in range(0, A.limit, 3)]
    for r in range(3, rMax):
        if len(A.P) == r:
            A.P += [ A.P[-1] * (A.rows[-1][0] - 1) ]  # A377469
            A.rows += [[]]; A.S += [ A.S[-1] * L[0] ] # ludic factorials
        if len(R := A.rows[r]) < A.P[r]: # append more terms to this row
            R += L[ L[0]*len(R) : A.S[r] : L[0] ]
        L = [x for i, x in enumerate(L) if i%L[0]] # M. F. Hasler, Nov 17 2024

(define (A255127 n) (if (<= n 1) n (A255127bi (A002260 (- n 1)) (A004736 (- n 1)))))
(define (A255127bi row col) ((rowfun_n_for_A255127 row) col))
;; definec-macro memoizes its results:
(definec (rowfun_n_for_A255127 n) (if (= 1 n) (lambda (n) (+ n n)) (let* ((rowfun_for_remaining (rowfun_n_for_remaining_numbers (- n 1))) (eka (rowfun_for_remaining 0))) (COMPOSE rowfun_for_remaining (lambda (n) (* eka (- n 1)))))))
(definec (rowfun_n_for_remaining_numbers n) (if (= 1 n) (lambda (n) (+ n n 3)) (let* ((rowfun_for_prevrow (rowfun_n_for_remaining_numbers (- n 1))) (off (rowfun_for_prevrow 0))) (COMPOSE rowfun_for_prevrow (lambda (n) (+ 1 n (floor->exact (/ n (- off 1)))))))))

From M. F. Hasler, Nov 12 2024: (Start)
A(r, c) = A(r, c-P(r)) + S(r) = A(r, ((c-1) mod P(r)) + 1) + floor((c-1)/P(r))*S(r) with periods P = (1, 1, 2, 8, 48, 480, 5760, ...) = A377469, and shifts S = (2, 6, 30, 210, 2310, 30030, 510510) = A376237(2, 3, ...). For example:
A(1, c) = A(1, c-1) + 2 = 2 + (c-1)*2 = 2*c,
A(2, c) = A(2, c-1) + 6 = 3 + (c-1)*6 = 6*c - 3,
A(3, c) = A(3, c-2) + 30 = {5 if c is odd else 19} + floor((c-1)/2)*30 = 15*c - 11 + (c mod 2),
A(4, c) = A(4, c-8) + 210 = A(4, ((c-1) mod 8)+1) + floor((c-1)/8)*210, etc. (End)

A219178 a(n) = first unlucky number removed at the n-th stage of Lucky sieve.

Original entry on oeis.org

2, 5, 19, 27, 45, 55, 85, 109, 139, 157, 175, 213, 255, 265, 337, 363, 387, 411, 423, 457, 513, 547, 597, 637, 675, 715, 789, 807, 843, 871, 907, 987, 1033, 1083, 1113, 1125, 1267, 1297, 1315, 1371, 1407, 1465, 1515, 1555, 1609, 1651, 1671, 1707, 1851, 1873, 1927, 1969

Offset: 1

Phil Carmody, Nov 15 2012

First numbers removed by each lucky number in the lucky number sieve. - This is the original definition of the sequence, still valid from a(2) onward.

a(1) = 2, because at the first stage of Lucky sieve, all even numbers are removed, of which 2 is the first one. - Antti Karttunen, Feb 26 2015

			1 and 2 are a special case in the lucky number sieve, (1 is the lucky number, but every 2nd element is removed) so are ignored [in the original version of the sequence, which started from a(2). Now we have a(1) = 2. - _Antti Karttunen_, Feb 26 2015]. The 2nd lucky number, 3, removes { 5, 11, ... } from the list, so a(2) = 5. The 3rd lucky number, 7, removes { 19, 39, ... } from the list, so a(3)=19.

Antti Karttunen, Table of n, a(n) for n = 1..333
Wikipedia, Lucky Number

Column 1 of A255543, Column 2 of A255545 (And apart from the first term, also column 2 of A255551).

Cf. A000959, A001248, A254100, A255549, A255550, A255553.

rows = 52; cols = 1; L = 2 Range[0, 10^4] + 1; A = Join[{2 Range[cols]}, Reap[For[n = 2, n <= rows, r = L[[n++]]; L0 = L; L = ReplacePart[L, Table[r i -> Nothing, {i, 1, Length[L]/r}]]; Sow[Complement[L0, L][[1 ;; cols]]]]][[2, 1]]]; Table[A[[n, 1]], {n, 1, rows}] (* Jean-François Alcover, Mar 15 2016 *)

(define (A219178 n) (A255543bi n 1)) ;; Code for A255543bi given in A255543.

From Antti Karttunen, Feb 26 2015: (Start)
a(n) = A255543(n,1).
Other identities.
For all n >= 2, a(n) = A255553(A001248(n)).
(End)

Term a(1) = 2 prepended, without changing the rest of sequence. Name changed, with the original, more restrictive definition moved to the Comments section. - Antti Karttunen, Feb 26 2015

A255407 Permutation of natural numbers: a(n) = A255127(A252460(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 20, 21, 22, 25, 24, 19, 26, 27, 28, 29, 30, 37, 32, 33, 34, 35, 36, 41, 38, 39, 40, 43, 42, 47, 44, 45, 46, 53, 48, 31, 50, 51, 52, 61, 54, 49, 56, 57, 58, 67, 60, 71, 62, 63, 64, 65, 66, 77, 68, 69, 70, 83, 72, 89, 74, 75, 76, 59, 78, 91, 80, 81

Offset: 1

Antti Karttunen, Feb 22 2015

nonn

a(n) tells which number in Ludic array A255127 is at the same position where n is in array A083221, the sieve of Eratosthenes. As both arrays have A005843 (even numbers) and A016945 as their two topmost rows, both sequences are among the fixed points of this permutation.

Equally: a(n) tells which number in array A255129 is at the same position where n is in the array A083140, as they are the transposes of above two arrays.

			A083221(8,1) = 19 and A255127(8,1) = 23, thus a(19) = 23.
A083221(9,1) = 23 and A255127(9,1) = 25, thus a(23) = 25.
A083221(3,2) = 25 and A255127(3,2) = 19, thus a(25) = 19.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Cf. A001248, A003309, A007310, A008578, A083221, A084967, A252460, A254100, A255413, A255127.
Inverse: A255408.
Similar permutations: A249818.

a(n) = A255127(A252460(n)).
Other identities. For all n >= 1:
a(2n) = 2n. [Fixes even numbers.]
a(3n) = 3n. [Fixes multiples of three.]
a(A008578(n)) = A003309(n). [Maps noncomposites to Ludic numbers.]
a(A001248(n)) = A254100(n). [Maps squares of primes to "postludic numbers".]
a(A084967(n)) = a(5*A007310(n)) = A007310((5*n)-3) = A255413(n). [Maps A084967 to A255413.]
(And similarly between other columns and rows of A083221 and A255127.)

cp's OEIS Frontend

A256487 a(n) = A254100(n) - A219178(n).

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A256482 a(n) = A254100(n) - A003309(n+1).

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A276606 First differences of postludic numbers: a(n) = A254100(1+n) - A254100(n).

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A256483 a(n) = A256482(n)/2 = (A254100(n) - A003309(n+1)) / 2.

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A256488 a(n) = A256487(n)/2 = (A254100(n) - A219178(n))/2.

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A276576 Column 2 of A276580: a(n) = A276570(A254100(n)); the n-th postludic number modulo the corresponding Ludic number.

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A003309 Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th remaining number.

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Haskell

Maple

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PARI

PARI

PARI

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Python

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A255127 Ludic array: square array A(row,col), where row n lists the numbers removed at stage n in the sieve which produces Ludic numbers. Array is read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

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