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A032745 Super-5 Numbers (5 * n^5 contains substring '55555' in its decimal expansion).

%I A032745 #32 Jul 15 2025 15:25:04
%S A032745 4602,5517,7539,12955,14555,20137,20379,26629,32767,35689,35825,37706,
%T A032745 46020,46715,51988,55170,66344,73338,73974,75390,76157,86025,91497,
%U A032745 105852,114488,129550,132234,145550,146399,158651,160897,171673,174782,176988,184471,188421,191261,192607
%N A032745 Super-5 Numbers (5 * n^5 contains substring '55555' in its decimal expansion).
%C A032745 The terms a({15, 25, 34}) = {51988, 114488, 176988} are such that 5*a(n)^5 == 55555840 (mod 10^8). Therefore any number congruent to one of these, modulo 5*10^5, is also in the sequence. Of course, for any a(n) in the sequence, any a(n)*10^k, k >= 0, is also in the sequence. - _M. F. Hasler_, Jul 16 2024
%C A032745 Conjecture: a(n) ~ n. - _Charles R Greathouse IV_, Dec 04 2024
%D A032745 C. A. Pickover, "Keys to Infinity", New York: Wiley, p. 7, 1995.
%H A032745 Robert Israel, <a href="/A032745/b032745.txt">Table of n, a(n) for n = 1..10000</a>
%H A032745 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/super-d_number/">super-d numbers</a>, personal web site "Numbers Aplenty", 2013
%H A032745 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Super-dNumber.html">Super-d Number</a>
%p A032745 filter:= proc(n) local S;
%p A032745   StringTools:-Search("55555",sprintf("%d",5*n^5))<> 0
%p A032745 end proc:
%p A032745 select(filter, [$1..200000]); # _Robert Israel_, Jul 14 2025
%t A032745 Select[Range[200000],SequenceCount[IntegerDigits[5#^5],{5,5,5,5,5}]>0&] (* _Harvey P. Dale_, Jul 16 2016 *)
%o A032745 (PARI) select( {is_A032745(n)=is_A032743(n, 5)}, [1..2^18]) \\ _M. F. Hasler_, Jul 16 2024
%Y A032745 Cf. A014569, A032743-A032749.
%K A032745 nonn,base
%O A032745 1,1
%A A032745 _Patrick De Geest_, May 15 1998
%E A032745 Offset changed to 1 by _Andrew Howroyd_, Jul 16 2024