cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A014569 #35 Feb 16 2025 08:32:33
%S A014569 261,462,471,481,558,753,1036,1046,1471,1645,1752,1848,1923,1926,1968,
%T A014569 2031,2231,2232,2363,2395,2471,2591,2610,3058,3087,3148,3163,3172,
%U A014569 3181,3471,3494,3542,3851,3884,4143,4269,4314,4471,4527,4554,4620,4710,4732
%N A014569 Super-3 Numbers (3n^3 contains substring '333' in its decimal expansion).
%C A014569 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 A014569 Conjecture: a(n) ~ n. - _Charles R Greathouse IV_, Dec 04 2024
%D A014569 C. A. Pickover, Keys to Infinity. New York: Wiley, p. 7, 1995.
%H A014569 Harvey P. Dale, <a href="/A014569/b014569.txt">Table of n, a(n) for n = 1..1000</a>
%H A014569 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/super-d_number/">super-d numbers</a>, personal web site "Numbers Aplenty", 2013.
%H A014569 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Super-dNumber.html">Super-d Number.</a>
%F A014569 n < a(n) < 200n for n > 2. - _Charles R Greathouse IV_, Dec 04 2024
%e A014569 1752 is in the sequence since 3 * 1752^3 = 161'333'13024.
%t A014569 Select[Range[5000],MemberQ[Partition[IntegerDigits[3#^3],3,1],{3,3,3}]&] (* _Harvey P. Dale_, Feb 01 2013 *)
%o A014569 (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 A014569 (Python) is_A014569=lambda n, d=3: str(d)*d in str(d*n**d) # _M. F. Hasler_, Jul 16 2024
%Y A014569 Cf. A032743-A032749 (similar for d=2, ..., 9).
%K A014569 nonn,base
%O A014569 1,1
%A A014569 _Eric W. Weisstein_
%E A014569 Corrected and extended by _Patrick De Geest_, May 15 1998
%E A014569 Offset changed to 1 by _M. F. Hasler_, Jul 16 2024