A032744 Super-4 Numbers (4 * n^4 contains substring '4444' in its decimal expansion).

1168, 4972, 7423, 7752, 8431, 10267, 11317, 11487, 11549, 11680, 16588, 16664, 16837, 18257, 18597, 19784, 19933, 22217, 22504, 22819, 22829, 24078, 24331, 24514, 25296, 25698, 26685, 26738, 27812, 27973, 28988, 32466, 32467, 32735, 34078, 34636, 35248, 36219, 36602

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Comments

a(17) = 19933 and a(20) = 22819 are such that a(n)^4 == 111121 (mod 10^6), therefore any number ending in (0|5)19933 or in (0|5)22819, where (a|b) means a or b, is in the sequence. Of course, for each 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

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• 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

Select[Range[33000],MemberQ[Partition[IntegerDigits[4*#^4],4,1],{4,4,4,4}]&] (* Harvey P. Dale, Mar 22 2012 *)

PARI

select( is_A032744(n)=is_A032743(n,4), [1..33333]) \\ M. F. Hasler, Jul 16 2024

Python

is_A032744=lambda n: '4444' in str(4*n**4) # M. F. Hasler, Jul 16 2024

Extensions

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