A105427 -id:A105427 - cp's OEIS frontend

A105428 Smallest prime dividing the composite near-repdigit number 133...33 consisting of a 1 followed by n 3's, where n=A105427.

7, 31, 67, 151, 23, 13, 7, 157, 163, 107, 17, 13, 7, 89, 170809, 31, 13, 7, 4363363, 251, 42169, 43, 13, 7, 641, 17, 6791, 109, 13, 7, 31, 29, 373, 261382937, 13, 7, 101921, 82647847, 443, 13, 7, 43, 1042402171, 71, 31, 13, 7, 1601, 425519761

Offset: 1

Lekraj Beedassy, Apr 08 2005

nonn

FactorDB, Factorizations of (10^n-1)/3+10^n
Makoto Kamada, Factorizations of 133...33.

Cf. A089018.

Transpose[FactorInteger[#]][[1,1]]&/@DeleteCases[Table[ FromDigits[ PadRight[{1},n,3]],{n,2,60}],?PrimeQ] (* _Harvey P. Dale, Dec 10 2011 *)

for(n=1,100,m=10^n+(10^n-1)/3;if(!isprime(m),print1(factorint(m)[1,1]," "))) (Alekseyev)

More terms from Max Alekseyev, Apr 11 2005

A051200 Except for initial term, primes of form "n 3's followed by 1".

Original entry on oeis.org

3, 31, 331, 3331, 33331, 333331, 3333331, 33333331, 333333333333333331, 3333333333333333333333333333333333333331, 33333333333333333333333333333333333333333333333331

Offset: 1

N. J. A. Sloane

"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

Martin Gardner, The Last Recreations, Chapter 12: Strong Laws of Small Primes, Springer-Verlag, 1997, pp. 191-205, especially 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

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.

Cf. A055520, A089017, A089018, A093671, A056698, A105427, A105428, A033175, A123568.

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

Union of 3 and A123568.

More terms from James Sellers

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

cp's OEIS Frontend

A105428 Smallest prime dividing the composite near-repdigit number 133...33 consisting of a 1 followed by n 3's, where n=A105427.

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