cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A089018 Smallest prime dividing the composite number consisting of A089017(n) successive 3's followed by a terminal 1.

Original entry on oeis.org

17, 673, 307, 19, 523, 607, 181, 199, 31, 1009, 29, 23, 177943, 61, 312929, 17, 821, 353, 363941, 829, 19, 686269, 31, 1019, 2761379, 145501, 1397023, 28529353, 47, 2543, 17, 439, 23, 59, 70717063, 15683, 31, 19, 4555681103, 10616546557, 28759, 83
Offset: 1

Views

Author

Lekraj Beedassy, Nov 04 2003

Keywords

Links

Programs

  • PARI
    do(lim)=my(v=List());for(n=9,lim+1,if(ispseudoprime(10^n\3-2), next); forprime(p=7,,if(Mod(10,p)^n==7,listput(v,p); next(2)))); Vec(v) \\ tests numbers with A089017(n) <= m; Charles R Greathouse IV, Oct 23 2013

Extensions

More terms from Ray Chandler, Nov 04 2003

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

Views

Author

N. J. A. Sloane

Keywords

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

  • 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

Links

Crossrefs

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

Programs

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

Formula

Union of 3 and A123568.

Extensions

More terms from James Sellers
Cross reference added by Harvey P. Dale, May 21 2014

A105427 Numbers n such that the near-repdigit number consisting of a 1 followed by n 3's (i.e., of form 1333...33) is composite.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
Offset: 1

Views

Author

Lekraj Beedassy, Apr 08 2005

Keywords

Comments

Complement of A056698.

Links

Crossrefs

Cf. A051200, A089017, A093671.

Programs

  • Mathematica
    Select[Range[100],CompositeQ[FromDigits[PadRight[{1},#,3]]]&]-1 (* Harvey P. Dale, Jul 23 2014 *)
  • PARI
    isok(n) = ! isprime(10^n+(10^n-1)/3) \\ Michel Marcus, Jul 28 2013
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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