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

1,1

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

Table of n, a(n) for n=1..22.

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A254779 A254725 A117225 * A180099 A092013 A186878

Adjacent sequences: A032745 A032746 A032747 * A032749 A032750 A032751

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Extensions

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

Status

approved