A032746 Super-6 Numbers (6 * n^6 contains substring '666666' in its decimal expansion).

27257, 272570, 302693, 323576, 364509, 502785, 513675, 537771, 676657, 678146, 731378, 831122, 836553, 913797, 920456, 921269, 1045361, 1144983, 1169054, 1283069, 1288697, 1292673, 1343642, 1346117, 1472078, 1523993, 1640026

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Comments

The terms a({5, 9, 11, 12}) = {364509, 676657, 731378, 831122} are such that 6*a(n)^6 == 66666646, 66666694, or 66666624 (mod 10^8). Therefore, any number congruent to one of these (mod 5*10^7) is also in the sequence. Of course, for any term a(n), all numbers a(n)*10^k, k >= 0, are 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

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

Crossrefs

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

Programs

Mathematica

With[{c=6},Select[Range[165*10^4],SequenceCount[IntegerDigits[c #^c],PadRight[ {},c,c]]>0&]] (* Harvey P. Dale, Jan 18 2023 *)

PARI

select( {is_A032746(n)=is_A014569(n,6)}, [1..10^5])
for(n=1, oo, is_A032746(n)&& print1(n", ")) \\ Quite slow... - M. F. Hasler, Jul 16 2024

Extensions

Offset changed to 1 by M. F. Hasler, Jul 16 2024