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A051200 Except for initial term, primes of form "n 3's followed by 1". 15
3, 31, 331, 3331, 33331, 333331, 3333331, 33333331, 333333333333333331, 3333333333333333333333333333333333333331, 33333333333333333333333333333333333333333333333331 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

"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

REFERENCES

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

LINKS

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.

FORMULA

Union of 3 and A123568.

MATHEMATICA

Join[{3}, Select[Rest[FromDigits/@Table[PadLeft[{1}, n, 3], {n, 50}]], PrimeQ]]  (* Harvey P. Dale, Apr 20 2011 *)

CROSSREFS

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

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers

Cross reference added by Harvey P. Dale, May 21 2014

STATUS

approved

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Last modified August 20 18:11 EDT 2019. Contains 326154 sequences. (Running on oeis4.)