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 A164841 Numbers whose squares have a digit average greater than 8. 4
 3, 94863, 987917, 3162083, 29983327, 99477133, 99483667, 994927133, 2428989417, 2754991833, 2983284917, 2999833327, 3157196367, 9380293167, 9486778167, 28105157886, 31144643167, 31304790167, 31459487917, 31464263856, 94286790167, 99497231067, 244272388937 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 12 04:50 EDT 2024. Contains 375085 sequences. (Running on oeis4.)