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

1,1

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

Table of n, a(n) for n=1..27.

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

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A250852 A157820 A251777 * A099230 A267706 A237381

Adjacent sequences: A032743 A032744 A032745 * A032747 A032748 A032749

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Extensions

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

Status

approved