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A032748 Super-8 Numbers (8 * n^8 contains substring '88888888' in its decimal expansion).

%I A032748 #29 Feb 16 2025 08:32:36
%S A032748 185423,641519,1551728,1854230,6415190,12043464,12147605,15517280,
%T A032748 16561735,18542300,26908132,29242698,33491333,34982204,35866945,
%U A032748 37584428,44263715,45980752,54555936,56148739,60883944,64151900
%N A032748 Super-8 Numbers (8 * n^8 contains substring '88888888' in its decimal expansion).
%C A032748 All numbers congruent to a(2) = 641519 (mod 5*10^10) are also in the sequence. - _M. F. Hasler_, Jul 17 2024
%C A032748 Conjecture: a(n) ~ n. - _Charles R Greathouse IV_, Dec 04 2024
%D A032748 C. A. Pickover, "Keys to Infinity", New York: Wiley, p. 7, 1995.
%H A032748 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/super-d_number/">super-d numbers</a>, personal web site "Numbers Aplenty", 2013
%H A032748 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Super-dNumber.html">Super-d Number.</a>
%p A032748 d := 8 ;
%p A032748 for n from 1 do
%p A032748         convert(d*n^d,base,10) ;
%p A032748         if verify([8,8,8,8,8,8,8,8],%,'sublist') then
%p A032748                 print(n) ;
%p A032748         end if;
%p A032748 end do: # _R. J. Mathar_, Jan 11 2013
%t A032748 Select[Range[65*10^6],SequenceCount[IntegerDigits[8*#^8],{8,8,8,8,8,8,8,8}]>0&] (* _Harvey P. Dale_, Dec 24 2016 *)
%o A032748 (PARI) \\ See A014569 (not very efficient for d=8).
%o A032748 (Python) # See A014569 (not very efficient for d=8).
%Y A032748 Cf. A014569 (similar for d=3), A032743 - A032749 (similar for d=2, ..., 9).
%K A032748 nonn,base
%O A032748 1,1
%A A032748 _Patrick De Geest_, May 15 1998
%E A032748 Offset changed to 1 by _M. F. Hasler_, Jul 17 2024