cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-13 of 13 results.

A117756 Squares for which the reversed sum of the digits is also a square.

Original entry on oeis.org

0, 1, 4, 9, 36, 64, 81, 100, 121, 144, 225, 324, 361, 400, 441, 576, 729, 900, 1089, 1225, 1296, 1521, 1764, 2025, 2116, 2304, 2601, 2916, 3025, 3249, 3600, 4356, 4761, 5041, 5184, 5625, 6084, 6400, 6561, 7056, 8100, 9216, 9801, 10000, 10201, 10404, 11025
Offset: 0

Views

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 14 2006

Keywords

Examples

			729 is in the sequence because (1)it is a square, (2)the sum of its digits is 7+2+9=18 and (3)18 reversed is 81, which is a square.

Crossrefs

Cf. A053057 (squares whose digit sum is also a square).

Programs

  • Mathematica
    Select[Range[105]^2, IntegerQ@ Sqrt@ FromDigits@ Reverse@ IntegerDigits@ # &[Total@ IntegerDigits@ #] &] (* Michael De Vlieger, Jan 15 2016 *)
  • PARI
    isok(n) = issquare(n) && issquare(eval(concat( Vecrev(Str(sumdigits(n)))))); \\ Michel Marcus, Jan 15 2016

Extensions

a(34) corrected by Vincenzo Librandi, Jan 15 2016

A168139 Squares whose sum and number of digits are also squares.

Original entry on oeis.org

0, 1, 4, 9, 1521, 1681, 2025, 2304, 2601, 3364, 3481, 3600, 4489, 4624, 5776, 5929, 7225, 7396, 8100, 8836, 9025, 100000000, 100020001, 100040004, 100060009, 100080016, 100100025, 100200100, 100220121, 100240144, 100260169, 100400400
Offset: 1

Views

Author

Zak Seidov, Nov 19 2009

Keywords

Examples

			1521=39^2, number of digits = 4, number of digits = 1+5+2+1=9.

Crossrefs

Subsequence of A053057 (with additional first term = 0).

Programs

  • PARI
    isok(n) = issquare(n) && issquare(sumdigits(n)) && issquare(length(Str(n))); \\ Michel Marcus, Oct 15 2013

A384296 Square numbers whose iterative sums of digits are squares.

Original entry on oeis.org

0, 1, 4, 9, 36, 81, 100, 121, 144, 225, 324, 400, 441, 900, 1521, 2025, 2304, 2601, 3600, 8100, 10000, 10201, 10404, 11025, 12100, 12321, 14400, 22500, 32400, 40000, 40401, 44100, 62001, 69696, 90000, 101124, 103041, 121104, 123201, 149769, 152100, 173889, 178929, 199809, 202500, 230400, 251001
Offset: 1

Views

Author

Huaineng He, May 24 2025

Keywords

Examples

			10201 = 101^2. 1+0+2+0+1 = 4, 4 = 2^2.
178929 = 423^2. 1+7+8+9+2+9 = 36, 36 = 6^2. 3+6 = 9, 9 = 3^2.

Crossrefs

Cf. A004159, A117676, A070027.
A subsequence of A053057.

Programs

  • Maple
    filter:= proc(n) local L,i,t;
  t:= n;
  do
    if not issqr(t) then return false fi;
    if t < 10 then return true fi;
    t:= convert(convert(t,base,10),`+`)
  od
end proc:
select(filter, [seq(i^2,i=0..1000)]); # Robert Israel, May 25 2025
  • Mathematica
    q[n_] := AllTrue[FixedPointList[DigitSum, n], IntegerQ[Sqrt[#]] &]; Select[Range[0, 500]^2, q] (* Amiram Eldar, May 25 2025 *)
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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