%I #35 Feb 16 2025 08:32:33

%S 261,462,471,481,558,753,1036,1046,1471,1645,1752,1848,1923,1926,1968,

%T 2031,2231,2232,2363,2395,2471,2591,2610,3058,3087,3148,3163,3172,

%U 3181,3471,3494,3542,3851,3884,4143,4269,4314,4471,4527,4554,4620,4710,4732

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

%C 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

%C Conjecture: a(n) ~ n. - _Charles R Greathouse IV_, Dec 04 2024

%D C. A. Pickover, Keys to Infinity. New York: Wiley, p. 7, 1995.

%H Harvey P. Dale, <a href="/A014569/b014569.txt">Table of n, a(n) for n = 1..1000</a>

%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/super-d_number/">super-d numbers</a>, personal web site "Numbers Aplenty", 2013.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Super-dNumber.html">Super-d Number.</a>

%F n < a(n) < 200n for n > 2. - _Charles R Greathouse IV_, Dec 04 2024

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

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

%o (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

%o (Python) is_A014569=lambda n, d=3: str(d)*d in str(d*n**d) # _M. F. Hasler_, Jul 16 2024

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

%K nonn,base

%O 1,1

%A _Eric W. Weisstein_

%E Corrected and extended by _Patrick De Geest_, May 15 1998

%E Offset changed to 1 by _M. F. Hasler_, Jul 16 2024