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A267768 Numbers whose base-8 representation is a square when read in base 10. 3
0, 1, 4, 14, 21, 30, 52, 64, 81, 100, 149, 174, 212, 241, 256, 289, 382, 405, 446, 532, 622, 661, 804, 849, 896, 1012, 1045, 1102, 1220, 1281, 1344, 1409, 1476, 1557, 1630, 1780, 1920, 2001, 2197, 2286, 2452, 2545, 2593, 2878, 2965, 3070, 3233, 3328, 3441, 3540, 3630, 3733, 4068, 4096 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Trivially includes powers of 64, since 64^k = 100..00_8 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 64*a(n) is also in the sequence. One could call "primitive" the terms not of this form. These primitive terms include the subsequence 64^k + 2*8^k + 1 = (8^k+1)^2, k > 0, which yields A033934 when written in base 8.

Motivated by the subsequence A267490 which lists the primes in this sequence.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

MATHEMATICA

Select[Range[0, 2 10^4], IntegerQ@Sqrt@FromDigits@IntegerDigits[#, 8] &] (* Vincenzo Librandi, Dec 28 2016 *)

PROG

(PARI) is(n, b=8, c=10)=issquare(subst(Pol(digits(n, b)), x, c))

(Python)

A267768_list = [int(s, 8) for s in (str(i**2) for i in range(10**6)) if max(s) < '8'] # Chai Wah Wu, Jan 20 2016

(MAGMA) [n: n in [0..10^4] | IsSquare(Seqint(Intseq(n, 8)))]; // Vincenzo Librandi, Dec 28 2016

CROSSREFS

Cf. A267763 - A267769 for bases 3 through 9. The base-2 analog is A000302 = powers of 4.

For a "prime" analog see also A235265, A235266, A152079, A235461 - A235482, A065720A036952, A065721 - A065727, A235394, A235395, A089971A020449, A089981, A090707 - A091924.

Sequence in context: A030470 A326004 A297358 * A185008 A165721 A197638

Adjacent sequences:  A267765 A267766 A267767 * A267769 A267770 A267771

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 20 2016

STATUS

approved

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Last modified May 7 22:52 EDT 2021. Contains 343652 sequences. (Running on oeis4.)