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Start of the first occurrence of exactly n consecutive squares with digit sum also a square.
2

%I #13 Aug 27 2018 16:54:04

%S 16,36,900,3364,0,123409881,10000,81,2120219933855716,

%T 91361386718598177458046950625

%N Start of the first occurrence of exactly n consecutive squares with digit sum also a square.

%e a(7) = 81 as the sums of the digits of the 7 consecutive squares 81, 100, 121, 144, 169, 196, 225 are squares, but the digit sums of 64 and 256 are not.

%t l[n_] := Module[{k}, For[k=0, IntegerQ[Sqrt[Plus@@IntegerDigits[(n+k)^2]]], k++, Null]; k]; Clear[a]; For[n=0, True, n+=ln+1, If[a[ln=l[n]]==-1, Null, Null, a[ln]=n; Print["a(", ln, ")=", n^2]]]

%Y Cf. A061910, A293832.

%K hard,more,nonn,base

%O 0,1

%A _Amarnath Murthy_, Mar 09 2002

%E Edited by _Dean Hickerson_, Oct 28 2002

%E a(9) from _Giovanni Resta_, Aug 27 2018