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

1,1

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

Table of n, a(n) for n=1..38.

Giovanni Resta, super-d numbers, personal web site "Numbers Aplenty", 2013

Eric Weisstein's World of Mathematics, Super-d Number

Mathematica

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

Prog

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

Crossrefs

Cf. A014569, A032743-A032749.

Sequence in context: A004537 A204655 A204652 * A020437 A157364 A035900

Adjacent sequences: A032742 A032743 A032744 * A032746 A032747 A032748

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Extensions

Offset changed to 1 by Andrew Howroyd, Jul 16 2024

Status

approved