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

185423, 641519, 1551728, 1854230, 6415190, 12043464, 12147605, 15517280, 16561735, 18542300, 26908132, 29242698, 33491333, 34982204, 35866945, 37584428, 44263715, 45980752, 54555936, 56148739, 60883944, 64151900

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Comments

All numbers congruent to a(2) = 641519 (mod 5*10^10) are also in the sequence. - M. F. Hasler, Jul 17 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

• Giovanni Resta, super-d numbers, personal web site "Numbers Aplenty", 2013
• Eric Weisstein's World of Mathematics, Super-d Number.

Crossrefs

Cf. A014569 (similar for d=3), A032743 - A032749 (similar for d=2, ..., 9).

Programs

Maple

d := 8 ;
for n from 1 do
        convert(d*n^d,base,10) ;
        if verify([8,8,8,8,8,8,8,8],%,'sublist') then
                print(n) ;
        end if;
end do: # R. J. Mathar, Jan 11 2013

Mathematica

Select[Range[65*10^6],SequenceCount[IntegerDigits[8*#^8],{8,8,8,8,8,8,8,8}]>0&] (* Harvey P. Dale, Dec 24 2016 *)

PARI

\\ See A014569 (not very efficient for d=8).

Python

# See A014569 (not very efficient for d=8).

Extensions

Offset changed to 1 by M. F. Hasler, Jul 17 2024