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.
%I A051200 #56 Jul 02 2025 16:01:58
%S A051200 3,31,331,3331,33331,333331,3333331,33333331,333333333333333331,
%T A051200 3333333333333333333333333333333333333331,
%U A051200 33333333333333333333333333333333333333333333333331
%N A051200 Except for initial term, primes of form "n 3's followed by 1".
%C A051200 "A remarkable pattern that is entirely accidental and leads nowhere" - M. Gardner, referring to the first 8 terms.
%C A051200 a(2)*a(3)*a(4) = 34179391, a Zeisel number (A051015) with coefficients (10,21).
%C A051200 a(2)*a(3)*a(4)*a(5) = 1139233281421, a Zeisel number with coefficients (10,21).
%C A051200 a(2)*a(3)*..*a(6) = 379741768929343351, a Zeisel number with coefficients (10,21).
%C A051200 a(2)*a(3)*..*a(7) = 1265805010367017001532181, a Zeisel number with coefficients (10,21).
%C A051200 a(2)*a(3)*..*a(8) = 42193497392022209194699696424911, a Zeisel number with coefficients (10,21).
%C A051200 Besides first 3, primes of the form (10^n-7)/3, n>1. See A123568. - _Vincenzo Librandi_, Aug 06 2010
%C A051200 The integer lengths of the terms of the sequence are 1, 2, 3, 4, 5, 6, 7, 8, 18, 40, 50, 60, 78, 101, 151, 319, 382, etc. - _Harvey P. Dale_, Dec 01 2018
%D A051200 Martin Gardner, The Last Recreations, Chapter 12: Strong Laws of Small Primes, Springer-Verlag, 1997, pp. 191-205, especially p. 194.
%D A051200 W. Sierpiński, 200 Zadan z Elementarnej Teorii Liczb, Warsaw, 1964; Problem 88 [in English: 200 Problems from the Elementary Theory of Numbers]
%D A051200 W. Sierpiński, 250 Problems in Elementary Number Theory. New York: American Elsevier, Warsaw, 1970, pp. 8, 56-57.
%D A051200 F. Smarandache, Properties of numbers, University of Craiova, 1973
%H A051200 R. K. Guy, <a href="/A005165/a005165.pdf">The strong law of small numbers</a>. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
%H A051200 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/3.html">3.</a>
%F A051200 Union of 3 and A123568.
%t A051200 Join[{3},Select[Rest[FromDigits/@Table[PadLeft[{1},n,3], {n,50}]], PrimeQ]] (* _Harvey P. Dale_, Apr 20 2011 *)
%Y A051200 Cf. A055520, A089017, A089018, A093671, A056698, A105427, A105428, A033175, A123568.
%K A051200 nonn,nice
%O A051200 1,1
%A A051200 _N. J. A. Sloane_
%E A051200 More terms from _James Sellers_
%E A051200 Cross reference added by _Harvey P. Dale_, May 21 2014