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A216446 Palindromic numbers which can be written as the sum of two or more consecutive squares. 3

%I #39 Oct 17 2021 11:26:17

%S 5,55,77,181,313,434,505,545,595,636,818,1001,1111,1441,1771,4334,

%T 6446,17371,17871,19691,21712,41214,42924,44444,46564,51015,65756,

%U 81818,97679,99199,108801,127721,137731,138831,139931,148841,161161,166661,171171,188881

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

%H V. Raman and Giovanni Resta, <a href="/A216446/b216446.txt">Table of n, a(n) for n = 1..10306</a> (terms < 10^18, first 298 terms from V. Raman)

%e 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.

%t 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 *)

%t With[{nn=200},Select[Union[Flatten[Table[Total/@Partition[Range[nn]^2,n,1],{n,2,nn}]]],PalindromeQ]] (* _Harvey P. Dale_, Oct 17 2021 *)

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

%K nonn,base

%O 1,1

%A _V. Raman_, Sep 07 2012

%E Errors in previous b-file noticed by _Riley Waugh_, Jun 13 2018

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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)