A068833 Start of the first occurrence of exactly n consecutive squares with digit sum also a square.

16, 36, 900, 3364, 0, 123409881, 10000, 81, 2120219933855716, 91361386718598177458046950625

Offset

0,1

Links

Table of n, a(n) for n=0..9.

Formula

a(n) >= A293832(n)^2 except for n = 4 (due to conventions), with equality for n = 7, 8, 9, and probably most of the subsequent terms. - M. F. Hasler, Oct 20 2025

Example

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.

Mathematica

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]]]

Prog

(PARI) apply( {A068833(n, k=0, is(x)=issquare(sumdigits(x^2)))=until(, forstep(j=n-1, 0, -1, is(k+j) || next(2+!k+=j+1)); is(k+n) || return(k^2); k+=n; while(is(k++), ))}, [0..8]) \\ M. F. Hasler, Oct 20 2025

Crossrefs

Cf. A061910, A293832 (k^2 is the start of a run of length >= n).

Sequence in context: A218523 A300535 A053893 * A116190 A070587 A350288

Adjacent sequences: A068830 A068831 A068832 * A068834 A068835 A068836

Keyword

hard,more,nonn,base

Author

Amarnath Murthy, Mar 09 2002

Extensions

Edited by Dean Hickerson, Oct 28 2002

a(9) from Giovanni Resta, Aug 27 2018

Status

approved