A216446 Palindromic numbers which can be written as the sum of two or more consecutive squares.

5, 55, 77, 181, 313, 434, 505, 545, 595, 636, 818, 1001, 1111, 1441, 1771, 4334, 6446, 17371, 17871, 19691, 21712, 41214, 42924, 44444, 46564, 51015, 65756, 81818, 97679, 99199, 108801, 127721, 137731, 138831, 139931, 148841, 161161, 166661, 171171, 188881

Offset

1,1

Links

V. Raman and Giovanni Resta, Table of n, a(n) for n = 1..10306 (terms < 10^18, first 298 terms from V. Raman)

Example

636 is in the sequence because it is a palindrome and 636 = 4^2+5^2+6^2+7^2+8^2+9^2+10^2+11^2+12^2.

Mathematica

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; upto = 10^6; Union[ Reap[ For[i=1, s=i^2 + (i+1)^2; s < upto, i++, For[j=i+1, s < upto, j++; s += j^2, If[palQ[s], Sow@ s]]]][[2, 1]]] (* Giovanni Resta, Jun 14 2018 *)
With[{nn=200}, Select[Union[Flatten[Table[Total/@Partition[Range[nn]^2, n, 1], {n, 2, nn}]]], PalindromeQ]] (* Harvey P. Dale, Oct 17 2021 *)

Crossrefs

Cf. A034705, A180436, A267600 (terms with more than one representation).

Sequence in context: A247711 A284066 A244439 * A307991 A015221 A035305

Adjacent sequences: A216443 A216444 A216445 * A216447 A216448 A216449

Keyword

nonn,base

Author

V. Raman, Sep 07 2012

Extensions

Errors in previous b-file noticed by Riley Waugh, Jun 13 2018

Status

approved