|
%I #52 Dec 01 2018 11:22:19
%S 3,31,331,3331,33331,333331,3333331,33333331,333333333333333331,
%T 3333333333333333333333333333333333333331,
%U 33333333333333333333333333333333333333333333333331
%N Except for initial term, primes of form "n 3's followed by 1".
%C "A remarkable pattern that is entirely accidental and leads nowhere" - M. Gardner, referring to the first 8 terms.
%C a(2)*a(3)*a(4) = 34179391, a Zeisel number (A051015) with coefficients (10,21).
%C a(2)*a(3)*a(4)*a(5) = 1139233281421, a Zeisel number with coefficients (10,21).
%C a(2)*a(3)*..*a(6) = 379741768929343351, a Zeisel number with coefficients (10,21).
%C a(2)*a(3)*..*a(7) = 1265805010367017001532181, a Zeisel number with coefficients (10,21).
%C a(2)*a(3)*..*a(8) = 42193497392022209194699696424911, a Zeisel number with coefficients (10,21).
%C Besides first 3, primes of the form (10^n-7)/3, n>1. See A123568. - _Vincenzo Librandi_, Aug 06 2010
%C 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 M. Gardner, The Last Recreations, Springer, 1997, p. 194.
%D W. Sierpiński, 200 Zadan z Elementarnej Teorii Liczb, Warsaw, 1964; Problem 88 [in English: 200 Problems from the Elementary Theory of Numbers]
%D W. Sierpiński, 250 Problems in Elementary Number Theory. New York: American Elsevier, Warsaw, 1970, pp. 8, 56-57.
%D F. Smarandache, Properties of numbers, University of Craiova, 1973
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/3.html">3.</a>
%F Union of 3 and A123568.
%t Join[{3},Select[Rest[FromDigits/@Table[PadLeft[{1},n,3], {n,50}]], PrimeQ]] (* _Harvey P. Dale_, Apr 20 2011 *)
%Y Cf. A055520, A089017, A089018, A093671, A056698, A105427, A105428, A033175, A123568.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_
%E Cross reference added by _Harvey P. Dale_, May 21 2014
|
