A014569 Super-3 Numbers (3n^3 contains substring '333' in its decimal expansion).

261, 462, 471, 481, 558, 753, 1036, 1046, 1471, 1645, 1752, 1848, 1923, 1926, 1968, 2031, 2231, 2232, 2363, 2395, 2471, 2591, 2610, 3058, 3087, 3148, 3163, 3172, 3181, 3471, 3494, 3542, 3851, 3884, 4143, 4269, 4314, 4471, 4527, 4554, 4620, 4710, 4732

Offset

1,1

Comments

For any term a(n), all numbers a(n)*10^k, k >= 0, are also in the sequence. More interestingly, all numbers N == 471 (mod 1000) are in the sequence, since 471^3*3 == 333 (mod 1000). - 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

Harvey P. Dale, 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.

Formula

n < a(n) < 200n for n > 2. - Charles R Greathouse IV, Dec 04 2024

Example

1752 is in the sequence since 3 * 1752^3 = 161'333'13024.

Mathematica

Select[Range[5000], MemberQ[Partition[IntegerDigits[3#^3], 3, 1], {3, 3, 3}]&] (* Harvey P. Dale, Feb 01 2013 *)

Prog

(PARI) select( {is_A014569(n, d=3, m=10^d, r=m\9*d)=n=d*n^d; until(r>n\=10, n%m==r && return(1))}, [0..4999]) \\ Using the (optional) 2nd arg d=2..9 allows to compute the sequences A032743-A032749. - M. F. Hasler, Jul 16 2024
(Python) is_A014569=lambda n, d=3: str(d)*d in str(d*n**d) # M. F. Hasler, Jul 16 2024

Crossrefs

Cf. A032743-A032749 (similar for d=2, ..., 9).

Sequence in context: A131062 A079506 A028527 * A063364 A264894 A028536

Adjacent sequences: A014566 A014567 A014568 * A014570 A014571 A014572

Keyword

nonn,base

Author

Eric W. Weisstein

Extensions

Corrected and extended by Patrick De Geest, May 15 1998

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

Status

approved