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%I #27 Dec 04 2024 09:51:09
%S 4602,5517,7539,12955,14555,20137,20379,26629,32767,35689,35825,37706,
%T 46020,46715,51988,55170,66344,73338,73974,75390,76157,86025,91497,
%U 105852,114488,129550,132234,145550,146399,158651,160897,171673,174782,176988,184471,188421,191261,192607
%N Super-5 Numbers (5 * n^5 contains substring '55555' in its decimal expansion).
%C 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 Conjecture: a(n) ~ n. - _Charles R Greathouse IV_, Dec 04 2024
%D C. A. Pickover, "Keys to Infinity", New York: Wiley, p. 7, 1995.
%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/super-d_number/">super-d numbers</a>, personal web site "Numbers Aplenty", 2013
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Super-dNumber.html">Super-d Number</a>
%t Select[Range[200000],SequenceCount[IntegerDigits[5#^5],{5,5,5,5,5}]>0&] (* _Harvey P. Dale_, Jul 16 2016 *)
%o (PARI) select( {is_A032745(n)=is_A032743(n, 5)}, [1..2^18]) \\ _M. F. Hasler_, Jul 16 2024
%Y Cf. A014569, A032743-A032749.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, May 15 1998
%E Offset changed to 1 by _Andrew Howroyd_, Jul 16 2024