A263612 -id:A263612 - cp's OEIS frontend

A029989 Squares which are palindromes in base 5.

0, 1, 4, 36, 676, 961, 4356, 15876, 24336, 391876, 423801, 571536, 646416, 9771876, 10732176, 14107536, 81974916, 244171876, 248094001, 264908176, 339812356, 351787536, 1061326084, 1167042244, 2181263616, 6103671876

Offset: 1

Patrick De Geest

Chai Wah Wu, Table of n, a(n) for n = 1..147
Patrick De Geest, Palindromic Squares in bases 2 to 17
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A002778, A003166, A263611, A263612, A029988.

pal5Q[n_]:=Module[{idn5=IntegerDigits[n,5]},idn5==Reverse[idn5]]; Select[ Range[0,80000]^2,pal5Q] (* Harvey P. Dale, May 05 2012 *)

A029988 Numbers k such that k^2 is palindromic in base 5.

Original entry on oeis.org

0, 1, 2, 6, 26, 31, 66, 126, 156, 626, 651, 756, 804, 3126, 3276, 3756, 9054, 15626, 15751, 16276, 18434, 18756, 32578, 34162, 46704, 78126, 78876, 81276, 93756, 390626, 391251, 393876, 406276, 468756, 487981, 1166454, 1953126, 1956876

Offset: 1

Patrick De Geest

Patrick De Geest, Palindromic Squares in bases 2 to 17
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A002778, A003166, A007091, A263611, A263612, A029989.

pal5Q[n_]:=Module[{idn5=IntegerDigits[n^2,5]},idn5==Reverse[idn5]]; Select[ Range[ 0,2*10^6],pal5Q] (* Harvey P. Dale, Feb 02 2023 *)

A263611 Base 5 numbers whose square is a palindrome in base 5.

Original entry on oeis.org

0, 1, 2, 11, 101, 111, 231, 1001, 1111, 10001, 10101, 11011, 11204, 100001, 101101, 110011, 242204, 1000001, 1001001, 1010101, 1042214, 1100011, 2020303, 2043122, 2443304, 10000001, 10011001, 10100101, 11000011, 100000001, 100010001, 100101001, 101000101, 110000011, 111103411

Offset: 1

N. J. A. Sloane, Oct 23 2015

A029988 expressed in base 5.

G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A007091, A002778, A029988, A263612, A029989.

With[{b = 5}, FromDigits@ IntegerDigits[#, b] & /@ Select[Range[b^9], PalindromeQ[IntegerDigits[#^2, b]] &]] (* Michael De Vlieger, Aug 15 2022 *)

a(n) = A007091(A029988(n)).

Name corrected by Charles R Greathouse IV, Aug 15 2022

cp's OEIS Frontend

A029989 Squares which are palindromes in base 5.

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A029988 Numbers k such that k^2 is palindromic in base 5.

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A263611 Base 5 numbers whose square is a palindrome in base 5.

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