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A051200
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Except for initial term, primes of form "n 3's followed by 1".
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16
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3, 31, 331, 3331, 33331, 333331, 3333331, 33333331, 333333333333333331, 3333333333333333333333333333333333333331, 33333333333333333333333333333333333333333333333331
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OFFSET
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1,1
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COMMENTS
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"A remarkable pattern that is entirely accidental and leads nowhere" - M. Gardner, referring to the first 8 terms.
a(2)*a(3)*a(4) = 34179391, a Zeisel number (A051015) with coefficients (10,21).
a(2)*a(3)*a(4)*a(5) = 1139233281421, a Zeisel number with coefficients (10,21).
a(2)*a(3)*..*a(6) = 379741768929343351, a Zeisel number with coefficients (10,21).
a(2)*a(3)*..*a(7) = 1265805010367017001532181, a Zeisel number with coefficients (10,21).
a(2)*a(3)*..*a(8) = 42193497392022209194699696424911, a Zeisel number with coefficients (10,21).
Besides first 3, primes of the form (10^n-7)/3, n>1. See A123568. - Vincenzo Librandi, Aug 06 2010
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
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REFERENCES
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M. Gardner, The Last Recreations, Springer, 1997, p. 194.
W. Sierpiński, 200 Zadan z Elementarnej Teorii Liczb, Warsaw, 1964; Problem 88 [in English: 200 Problems from the Elementary Theory of Numbers]
W. Sierpiński, 250 Problems in Elementary Number Theory. New York: American Elsevier, Warsaw, 1970, pp. 8, 56-57.
F. Smarandache, Properties of numbers, University of Craiova, 1973
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LINKS
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Table of n, a(n) for n=1..11.
R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
Eric Weisstein's World of Mathematics, 3.
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FORMULA
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Union of 3 and A123568.
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MATHEMATICA
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Join[{3}, Select[Rest[FromDigits/@Table[PadLeft[{1}, n, 3], {n, 50}]], PrimeQ]] (* Harvey P. Dale, Apr 20 2011 *)
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CROSSREFS
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Cf. A055520, A089017, A089018, A093671, A056698, A105427, A105428, A033175, A123568.
Sequence in context: A210852 A152276 A136024 * A274667 A136596 A186207
Adjacent sequences: A051197 A051198 A051199 * A051201 A051202 A051203
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from James A. Sellers
Cross reference added by Harvey P. Dale, May 21 2014
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STATUS
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approved
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