A007961 -id:A007961 - cp's OEIS frontend

A376358 Positions of numbers in A007961 that end in 1.

1, 5, 10, 14, 17, 21, 26, 30, 35, 37, 41, 46, 50, 54, 59, 63, 65, 69, 74, 78, 82, 86, 91, 95, 98, 101, 105, 110, 114, 117, 122, 126, 131, 135, 138, 142, 145, 149, 154, 158, 161, 165, 170, 174, 179, 183, 186, 190, 195, 197, 201, 206, 210, 213, 217, 222, 226

Offset: 1

Clark Kimberling, Sep 25 2024

Every positive integer is in exactly one of these sequences: A376358, this sequence, A376359, or A376360.

Conjecture: {a(n+1) - a(n) : n >= 1} = {2,3,4,5,6,7}. (See related conjectures at A376357, A376359, and A376360.)

Cf. A007961, A376354, A376357, A376359, A376360.

a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,
Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376357 *)
p1 = Flatten[Position[m, 1]]  (* this sequence *)
p2 = Flatten[Position[m, 2]]  (* A376359 *)
p3 = Flatten[Position[m, 3]]  (* A376360 *)
(* Peter J. C. Moses, Sep 20 2024 *)

A376359 Positions of numbers in A007961 that end in 2.

Original entry on oeis.org

2, 6, 11, 15, 18, 22, 27, 31, 38, 42, 47, 51, 55, 60, 66, 70, 75, 79, 83, 87, 92, 96, 99, 102, 106, 111, 115, 118, 123, 127, 132, 136, 139, 143, 146, 150, 155, 159, 162, 166, 171, 175, 180, 184, 187, 191, 198, 202, 207, 211, 214, 218, 223, 227, 231, 236, 240

Offset: 1

Clark Kimberling, Sep 25 2024

Every positive integer is in exactly one of these sequences: A376357, A376358, this sequence, or A376360.

Conjecture: {a(n+1) - a(n) : n >= 1} = {3,4,5,6,7,8,9,10}. (See related conjectures at A376357, A376358, and A376360.)

Cf. A007961, A376354, A376357, A376358, A376360.

a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,
Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376357 *)
p1 = Flatten[Position[m, 1]]  (* A376359 *)
p2 = Flatten[Position[m, 2]]  (* this sequence *)
p3 = Flatten[Position[m, 3]]  (* A376360 *)
(* Peter J. C. Moses, Sep 20 2024 *)

A376360 Positions of numbers in A007961 that end in 3.

Original entry on oeis.org

3, 7, 12, 19, 23, 28, 32, 39, 43, 48, 52, 56, 61, 67, 71, 76, 84, 88, 93, 103, 107, 112, 119, 124, 128, 133, 140, 147, 151, 156, 163, 167, 172, 176, 181, 188, 192, 199, 203, 208, 215, 219, 224, 228, 232, 237, 244, 248, 253, 259, 263, 268, 275, 279, 284, 288

Offset: 1

Clark Kimberling, Sep 25 2024

Every positive integer is in exactly one of these sequences: A376357, A376358, A376359, or this sequence.

Conjecture: {a(n+1) - a(n) : n >= 1} = {4,5,6,7,8,9,10,11,13}. It has been checked that a(n+1) - a(n) is not 12 for 1<=n<=300000. (See related conjectures at A376357, A376358, and A376359.)

Cf. A007961, A376354, A376357, A376358, A376359.

a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,
Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376357 *)
p1 = Flatten[Position[m, 1]]  (* A376358 *)
p2 = Flatten[Position[m, 2]]  (* A376359 *)
p3 = Flatten[Position[m, 3]]  (* this sequence *)
(* Peter J. C. Moses, Sep 20 2024 *)

A000196 Integer part of square root of n. Or, number of positive squares <= n. Or, n appears 2n+1 times.

Original entry on oeis.org

0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10

Offset: 0

N. J. A. Sloane

Also the integer part of the geometric mean of the divisors of n. - Amarnath Murthy, Dec 19 2001
Number of numbers k (<= n) with an odd number of divisors. - Benoit Cloitre, Sep 07 2002
Also, for n > 0, the number of digits when writing n in base where place values are squares, cf. A007961; A190321(n) <= a(n). - Reinhard Zumkeller, May 08 2011
The least monotonic left inverse of squares, A000290. That is, the lexicographically least nondecreasing sequence a(n) such that a(A000290(n)) = n. - Antti Karttunen, Oct 06 2017

			G.f. = x + x^2 + x^3 + 2*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + 2*x^8 + 3*x^9 + ...

Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, p. 73, problem 23.
Lionel Levine, Fractal sequences and restricted Nim, Ars Combin. 80 (2006), 113-127.
Paul J. McCarthy, Introduction to Arithmetical Functions, Springer Verlag, 1986, p. 28.
N. J. A. Sloane and Allan Wilks, On sequences of Recaman type, paper in preparation, 2006.

Franklin T. Adams-Watters, Table of n, a(n) for n = 0..10000
Krassimir Atanassov, On Some of Smarandache's Problems
Krassimir Atanassov, On the 100-th, the 101-st and 102-nd Smarandache's problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 3, 94-96.
Henry Bottomley, Illustration of A000196, A048760, A053186.
Matthew Hyatt and Marina Skyers, On the Increases of the Sequence floor(k*sqrt(n)), Electronic Journal of Combinatorial Number Theory, Volume 15 (2015), #A17.
Lionel Levine, Fractal sequences and restricted Nim, arXiv:math/0409408 [math.CO], 2004.
Paul Pollack and Joseph Vandehey, Besicovitch, Bisection, and the Normality of 0.(1)(4)(9)(16)(25)...., The American Mathematical Monthly 122.8 (2015): 757-765.
N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)
Florentin Smarandache, Only Problems, Not Solutions!, 1993.

Cf. A000290, A002162, A003056, A028391, A048760, A048766, A074704, A079051.

Column k=1 of A281871.

import Data.Bits (shiftL, shiftR)
a000196 :: Integer -> Integer
a000196 0 = 0
a000196 n = newton n (findx0 n 1) where
   -- find x0 == 2^(a+1), such that 4^a <= n < 4^(a+1).
   findx0 0 b = b
   findx0 a b = findx0 (a `shiftR` 2) (b `shiftL` 1)
   newton n x = if x' < x then newton n x' else x
                where x' = (x + n `div` x) `div` 2
a000196_list = concat $ zipWith replicate [1,3..] [0..]
-- Reinhard Zumkeller, Apr 12 2012, Oct 23 2010

a(n) = isqrt(n) # Paul Muljadi, Jun 03 2024

Magma
```
[Isqrt(n) : n in [0..100]];
```

Digits := 100; A000196 := n->floor(evalf(sqrt(n)));

Table[n, {n, 0, 20}, {2n + 1}] //Flatten (* Zak Seidov Mar 19 2011 *)
IntegerPart[Sqrt[Range[0, 110]]] (* Harvey P. Dale, May 23 2012 *)
Floor[Sqrt[Range[0, 99]]] (* Alonso del Arte, Dec 31 2013 *)
a[ n_] := SeriesCoefficient[ (EllipticTheta[ 3, 0, x]  - 1) / (2 (1 - x)), {x, 0, n}]; (* Michael Somos, May 28 2014 *)

PARI
```
{a(n) = if( n<0, 0, sqrtint(n))};
```

# from http://code.activestate.com/recipes/577821-integer-square-root-function/
def A000196(n):
  if n < 0:
    raise ValueError('only defined for nonnegative n')
  if n == 0:
    return 0
  a, b = divmod(n.bit_length(), 2)
  j = 2**(a+b)
  while True:
    k = (j + n//j)//2
    if k >= j:
      return j
    j = k
print([A000196(n)for n in range(102)])
# Jason Kimberley, Nov 09 2016

from math import isqrt
def a(n): return isqrt(n)
print([a(n) for n in range(102)]) # Michael S. Branicky, Feb 15 2023

;; The following implementation uses higher order function LEFTINV-LEASTMONO-NC2NC from my IntSeq-library. It returns the least monotonic left inverse of any strictly growing function (see the comment-section for the definition) and although it does not converge as fast to the result as many specialized integer square root algorithms, at least it does not involve any floating point arithmetic. Thus with correctly implemented bignums it will produce correct results even with very large arguments, in contrast to just taking the floor of (sqrt n).
;; Source of LEFTINV-LEASTMONO-NC2NC can be found under https://github.com/karttu/IntSeq/blob/master/src/Transforms/transforms-core.ss and the definition of A000290 is given under that entry.
(define A000196 (LEFTINV-LEASTMONO-NC2NC 0 0 A000290)) ;; Antti Karttunen, Oct 06 2017

a(n) = Card(k, 0 < k <= n such that k is relatively prime to core(k)) where core(x) is the squarefree part of x. - Benoit Cloitre, May 02 2002
a(n) = a(n-1) + floor(n/(a(n-1)+1)^2), a(0) = 0. - Reinhard Zumkeller, Apr 12 2004
From Hieronymus Fischer, May 26 2007: (Start)
a(n) = Sum_{k=1..n} A010052(k).
G.f.: g(x) = (1/(1-x))*Sum_{j>=1} x^(j^2) = (theta_3(0, x) - 1)/(2*(1-x)) where theta_3 is a Jacobi theta function. (End)
a(n) = floor(A000267(n)/2). - Reinhard Zumkeller, Jun 27 2011
a(n) = floor(sqrt(n)). - Arkadiusz Wesolowski, Jan 09 2013
Sum_{n>0} 1/a(n)^s = 2*zeta(s-1) + zeta(s), where zeta is the Riemann zeta function. - Enrique Pérez Herrero, Oct 15 2013
From Wesley Ivan Hurt, Dec 31 2013: (Start)
a(n) = Sum_{i=1..n} (A000005(i) mod 2), n > 0.
a(n) = (1/2)*Sum_{i=1..n} (1 - (-1)^A000005(i)), n > 0. (End)
a(n) = sqrt(A048760(n)), n >= 0. - Wolfdieter Lang, Mar 24 2015
a(n) = Sum_{k=1..n} floor(n/k)*lambda(k) = Sum_{m=1..n} Sum_{d|m} lambda(d) where lambda(j) is Liouville lambda function, A008836. - Geoffrey Critzer, Apr 01 2015
Sum_{n>=1} (-1)^(n+1)/a(n) = log(2) (A002162). - Amiram Eldar, May 02 2023

A053610 Number of positive squares needed to sum to n using the greedy algorithm.

Original entry on oeis.org

1, 2, 3, 1, 2, 3, 4, 2, 1, 2, 3, 4, 2, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 5, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 5, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 5, 3, 4, 5, 2, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 5, 3, 4, 5, 2, 3, 4, 1, 2, 3, 4

Offset: 1

Jud McCranie, Mar 19 2000

nonn

Define f(n) = n - x^2 where (x+1)^2 > n >= x^2. a(n) = number of iterations in f(...f(f(n))...) to reach 0.
a(n) = 1 iff n is a perfect square.
Also sum of digits when writing n in base where place values are squares, cf. A007961. - Reinhard Zumkeller, May 08 2011
The sequence could have started with a(0)=0. - Thomas Ordowski, Jul 12 2014
The sequence is not bounded, see A006892. - Thomas Ordowski, Jul 13 2014

			7=4+1+1+1, so 7 requires 4 squares using the greedy algorithm, so a(7)=4.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A006892 (positions of records), A055401, A007961.

Cf. A000196, A000290, A057945 (summing triangular numbers).

a053610 n = s n $ reverse $ takeWhile (<= n) $ tail a000290_list where
  s _ []                 = 0
  s m (x:xs) | x > m     = s m xs
             | otherwise = m' + s r xs where (m',r) = divMod m x
-- Reinhard Zumkeller, May 08 2011

A053610 := proc(n)
    local a,x;
    a := 0 ;
    x := n ;
    while x > 0 do
        x := x-A048760(x) ;
        a := a+1 ;
    end do:
    a ;
end proc: # R. J. Mathar, May 13 2016

f[n_] := (n - Floor[Sqrt[n]]^2); g[n_] := (m = n; c = 1; While[a = f[m]; a != 0, c++; m = a]; c); Table[ g[n], {n, 1, 105}]

A053610(n,c=1)=while(n-=sqrtint(n)^2,c++);c \\ M. F. Hasler, Dec 04 2008

from math import isqrt
def A053610(n):
    c = 0
    while n:
        n -= isqrt(n)**2
        c += 1
    return c # Chai Wah Wu, Aug 01 2023

a(n) = A007953(A007961(n)). - Henry Bottomley, Jun 01 2000
a(n) = a(n - floor(sqrt(n))^2) + 1 = a(A053186(n)) + 1 [with a(0) = 0]. - Henry Bottomley, May 16 2000
A053610 = A002828 + A062535. - M. F. Hasler, Dec 04 2008

A265747 Numbers written in Jacobsthal greedy base.

Original entry on oeis.org

0, 1, 2, 10, 11, 100, 101, 102, 110, 111, 200, 1000, 1001, 1002, 1010, 1011, 1100, 1101, 1102, 1110, 1111, 10000, 10001, 10002, 10010, 10011, 10100, 10101, 10102, 10110, 10111, 10200, 11000, 11001, 11002, 11010, 11011, 11100, 11101, 11102, 11110, 11111, 20000, 100000, 100001, 100002, 100010, 100011, 100100

Offset: 0

Antti Karttunen, Dec 17 2015

These are called "Jacobsthal Representation Numbers" in Horadam's 1996 paper.
Sum_{i=0..} digit(i)*A001045(2+digit(i)) recovers n from such representation a(n), where digit(0) stands for the least significant digit (at the right), and A001045(k) gives the k-th Jacobsthal number.
No larger digits than 2 will occur, which allows representing the same sequence in a more compact form by base-3 coding in A265746.
Sequence A197911 gives the terms with no digit "2" in their representation, while its complement A003158 gives the terms where "2" occurs at least once.
Numbers beginning with digit "2" in this representation are given by A020988(n) [= 2*A002450(n) = 2*A001045(2n)].

			For n=7, when selecting the terms of A001045 with the greedy algorithm, we need terms A001045(4) + A001045(2) + A001045(2) = 5 + 1 + 1, thus a(7) = "102".
For n=10, we need A001045(4) + A001045(4) = 5+5, thus a(10) = "200".

Antti Karttunen, Table of n, a(n) for n = 0..10923
A. F. Horadam, Jacobsthal Representation Numbers, Fib Quart. 34 (1996), 40-54. (See especially page 50, which is page 11 in PDF.)

Cf. A001045, A002450, A020988, A007089, A197911, A003158.
Cf. A265745 (sum of digits).
Cf. A265746 (same numbers interpreted in base-3, then shown in decimal).
Cf. A084639 (positions of repunits).
Cf. A007961, A014417, A014418, A244159 for analogous sequences.

jacob[n_] := (2^n - (-1)^n)/3; maxInd[n_] := Floor[Log2[3*n + 1]]; A265747[n_] := A265747[n] = 10^(maxInd[n] - 2) + A265747[n - jacob[maxInd[n]]]; A265747[0] = 0; Array[A265747, 100, 0] (* Amiram Eldar, Jul 21 2023 *)

A130249(n) = floor(log(3*n + 1) / log(2));
A001045(n) = (2^n - (-1)^n) / 3;
A265747(n) = {if(n==0, 0, my(d=n - A001045(A130249(n))); 10^(A130249(n)-2) + if(d == 0, 0, A265747(d)));} \\ Amiram Eldar, Jul 21 2023

def greedyJ(n): m = (3*n+1).bit_length() - 1; return (m, (2**m-(-1)**m)//3)
def a(n):
    if n == 0: return 0
    place, value = greedyJ(n)
    return 10**(place-2) + a(n - value)
print([a(n) for n in range(49)]) # Michael S. Branicky, Jul 11 2021

a(0) = 0; for n >= 1, a(n) = 10^(A130249(n)-2) + a(n-A001045(A130249(n))).

a(n) = A007089(A265746(n)).

A276326 Numbers expressed in greedy A001563-base.

Original entry on oeis.org

0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 40, 41, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 123, 130, 131, 132, 133, 140, 141, 200, 201, 202, 203, 210, 211, 212, 213, 220, 221, 222, 223, 230, 231, 232, 233, 240, 241, 300, 301, 302, 303, 310, 311, 312, 313, 320, 321, 322, 323, 330, 331, 332, 333, 340, 341, 400

Offset: 0

Antti Karttunen, Aug 30 2016

Terms A001563(1) = 1, A001563(2) = 4, A001563(3) = 18, ... give the base values for the digit positions from 1 onward. Digit places are filled by always trying to find the largest possible term of A001563 that still fits into the sum.

A130744(8) = 3225600 = 10*A001563(8) is the first number which yields an ambiguous representation when expressed in decimal, because in this base it is actually "A0000000" (where digit "A" stands for ten).

			To recover n from a(n) the digits in positions i = 1, 2, 3, ... (starting indexing from the least significant digit at right) are multiplied by A001563(i) and added together:
  ----------------
   n         a(n)
  ----------------
   0           0
   1           1
   2           2
   3           3
   4          10
   5          11
   6          12
   7          13
   8          20
   9          21
  10          22
  11          23
  12          30
  13          31
  14          32
  15          33
  16          40
  17          41 (as 4*A001563(2) + 1*A001563(1) = 17)
  18         100 (as 1*A001563(3) + 0*A001563(2) + 0*A001563(1) = 18)
and:
3225599 99111111 (as 3225599 = 9*b(8) + 9*b(7) + b(6) + b(5) + b(4) + b(3) + b(2) + b(1)), where b(n) = A001563(n).

Antti Karttunen, Table of n, a(n) for n = 0..4320

Cf. A001563, A130744, A258198, A276335.
Cf. A276327 (the least significant nonzero digit).
Cf. A276328 (the sum of digits).
Cf. A276333 (the most significant digit).
Cf. A276336 (a largest digit).
Cf. A276337 (number of nonzero digits).
Cf. A033312 (repunits).
Cf. A276091 (no digits larger than one).
Differs from A007090 for the first time at n=16 and from A055655 at n=18.
Cf. also A007623, A007961, A000433, A014418, A265747.

f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], (# #!) &[# - i]]], {i, 0, # - 1}] &@ NestWhile[# + 1 &, 0, (# #!) &[# + 1] <= n &]; Rest[a][[All, 1]]]; Table[FromDigits@ f@ n, {n, 72}] (* Michael De Vlieger, Aug 31 2016 *)

(define (A276326 n) (let loop ((n n) (s 0)) (if (zero? n) s (let ((dig (A276333 n))) (if (> dig 9) (error "A276326: ambiguous representation of n, digit > 9 would be needed: " n dig) (loop (A276335 n) (+ s (* dig (expt 10 (- (A258198 n) 1))))))))))

A000433 n written in base where place values are positive cubes.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 100, 101, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 116, 117, 120, 121, 122, 123, 124, 125, 126, 127, 130, 131, 132, 200, 201, 202, 203

Offset: 0

R. Muller

Let [d1, d2, d3, ...] be the decimal expansion of the n-th term, then dk is the number of times that the greedy algorithm subtracts the cube k^3 with input n. - Joerg Arndt, Nov 21 2014
For n > 1: A048766(n) = number of digits of a(n); A190311(n) = number of nonzero digits of a(n); A055401(n) = sum of digits of a(n). - Reinhard Zumkeller, May 08 2011
First differs from numbers written in base 8 (A007094) at a(27) = 100, whereas A007094(27) = 33. - Alonso del Arte, Nov 27 2014
The rightmost (least significant) digit never exceeds 7, the second digit from the right never exceeds 3, the third digit never exceeds 2, and the rest are just 0's and 1's. - Ivan Neretin, Sep 03 2015

			a(26) = 32 because 26 = 3 * 2^3 + 2 * 1^3.
a(27) = 100 because 27 = 3^3 + 0 * 2^3 + 0 * 1^3.
a(28) = 101 because 28 = 3^3 + 0 * 2^3 + 1 * 1^3.

Florentin Smarandache, "Properties of the Numbers", University of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A000578, A007961.

import Data.Char (intToDigit)
a000433 0 = 0
a000433 n = read $ map intToDigit $
  t n $ reverse $ takeWhile (<= n) $ tail a000578_list where
      t _ []          = []
      t m (x:xs)
          | x > m     = 0 : t m xs
          | otherwise = (fromInteger m') : t r xs where (m',r) = divMod m x
-- Reinhard Zumkeller, May 08 2011

cp's OEIS Frontend

A376357 Positions of numbers in A007961 that end in 0.

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A190321 Number of nonzero digits when writing n in base where place values are squares, cf. A007961.

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A376358 Positions of numbers in A007961 that end in 1.

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A376359 Positions of numbers in A007961 that end in 2.

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A376360 Positions of numbers in A007961 that end in 3.

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A000196 Integer part of square root of n. Or, number of positive squares <= n. Or, n appears 2n+1 times.

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A053610 Number of positive squares needed to sum to n using the greedy algorithm.

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A265747 Numbers written in Jacobsthal greedy base.

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