A164841 Numbers whose squares have a digit average greater than 8.

3, 94863, 987917, 3162083, 29983327, 99477133, 99483667, 994927133, 2428989417, 2754991833, 2983284917, 2999833327, 3157196367, 9380293167, 9486778167, 28105157886, 31144643167, 31304790167, 31459487917, 31464263856, 94286790167, 99497231067, 244272388937

Offset

1,1

Comments

There are just 13 terms < 32*10^8.

3 is the only term whose square has a digit average that is an integer.

The squares of the first few terms have digit averages 9, 8.1, 8.08333, 8.15385, 8.06667, 8.125, 8.125, 8.22222, 8.05263, 8.05263, 8.10526, 8.10526, 8.05263, ...

The sequence contains all numbers of the form floor(30*100^k - 10^k*5/3), k > 5. As of today, we know of only 9 numbers whose square has a digit mean above 8.25: 3, 707106074079263583, 943345110232670883, 94180040294109027313, 2976388751488907738914, 312713447088224669275583, 893241282627485818275387, 314610537013606681884298837387 and 9984988582817657883693383344833. - M. F. Hasler, Apr 11 and Apr 13 2023

Links

Table of n, a(n) for n=1..23.

Ed Pegg, 314610537013606681884298837387, math-fun mailing list, April 11, 2023.

Prog

(PARI) for(L=1, oo, for(n=sqrtint(10^(L-1)-1)+1, sqrtint(10^L-1), sumdigits(n^2) > 8*L && print1(n", "))) \\ M. F. Hasler, Apr 11 2023

Crossrefs

Cf. A164771 (s=1), A164770 (s=2), A164782 (s=3), A164776 (s=4), A164774 (s=5), A164779 (s=6), A164773 (s=7), A164772 (s=8).

Cf. A164842 (s < 1).

Sequence in context: A213000 A151594 A119119 * A171366 A292691 A086785

Adjacent sequences: A164838 A164839 A164840 * A164842 A164843 A164844

Keyword

base,nonn

Author

Zak Seidov, Aug 28 2009

Extensions

a(14)-a(23) from Lars Blomberg, Apr 29 2013

Status

approved