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

4602, 5517, 7539, 12955, 14555, 20137, 20379, 26629, 32767, 35689, 35825, 37706, 46020, 46715, 51988, 55170, 66344, 73338, 73974, 75390, 76157, 86025, 91497, 105852, 114488, 129550, 132234, 145550, 146399, 158651, 160897, 171673, 174782, 176988, 184471, 188421, 191261, 192607

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Comments

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

Conjecture: a(n) ~ n. - Charles R Greathouse IV, Dec 04 2024

References

• C. A. Pickover, "Keys to Infinity", New York: Wiley, p. 7, 1995.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Giovanni Resta, super-d numbers, personal web site "Numbers Aplenty", 2013
• Eric Weisstein's World of Mathematics, Super-d Number

Crossrefs

Cf. A014569, A032743-A032749.

Programs

Maple

filter:= proc(n) local S;
  StringTools:-Search("55555",sprintf("%d",5*n^5))<> 0
end proc:
select(filter, [$1..200000]); # Robert Israel, Jul 14 2025

Mathematica

Select[Range[200000],SequenceCount[IntegerDigits[5#^5],{5,5,5,5,5}]>0&] (* Harvey P. Dale, Jul 16 2016 *)

PARI

select( {is_A032745(n)=is_A032743(n, 5)}, [1..2^18]) \\ M. F. Hasler, Jul 16 2024

Extensions

Offset changed to 1 by Andrew Howroyd, Jul 16 2024