A032747 Super-7 Numbers (7 * n^7 contains substring '7777777' in its decimal expansion).

140997, 490996, 1184321, 1259609, 1409970, 1783166, 1886654, 1977538, 2457756, 2714763, 2750425, 2980991, 3043607, 3283057, 3689639, 4191601, 4258476, 4642725, 4909960, 4973029, 5242829, 5349973, 5444788, 5523544, 5682065

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Comments

The term a(6) = 1783166 is such that 7*a(6)^7 == 777777792 (mod 10^9). Therefore, all numbers congruent to a(6) (mod 5*10^8) are 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 (d=2) - A032749 (d=9).

Programs

Mathematica

Select[Range[6*10^6],MemberQ[Partition[IntegerDigits[7#^7],7,1],{7,7,7,7,7,7,7}]&] (* Harvey P. Dale, Sep 01 2014 *)

PARI

is_A032747(n)=is_A014569(n, 7)
for(n=1,oo, is_A032747(n)&& print1(n", ")) \\ Quite slow, even to get the first few terms. - M. F. Hasler, Jul 16 2024