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

1,1

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A221350 A227485 A252009 * A185477 A185469 A065656

Adjacent sequences: A032741 A032742 A032743 * A032745 A032746 A032747

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Extensions

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

Status

approved