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.

A103783 Primes of the form primorial P(k)*n-1 with minimal n, n>0, k>=2.

Original entry on oeis.org

5, 29, 419, 2309, 30029, 1021019, 19399379, 669278609, 38818159379, 601681470389, 14841476269619, 304250263527209, 235489703970060539, 1844669347765474229, 228124109340330313109, 24995884552004764307909
Offset: 1

Views

Author

Lei Zhou, Feb 15 2005

Keywords

Comments

Weak conjecture: sequence is defined for all k>=2; strong conjecture: n<(prime(k))^2;
Smallest prime p such that the prime factorization of p+1 contains the first n+1 primes. - R. J. Mathar, Jul 03 2012

Examples

			P(2)*1-1=5 is prime, so a(2)=5;
P(9)*3-1=669278609 is prime, so a(9)=669278609;

Crossrefs

Cf. A002110, A103515, A103782, A073917, A214089.

Programs

  • Mathematica
    nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[(tt <= (Prime[n])^2) && (! (PrimeQ[cp])), tt = tt + 1; cp = npd*tt - 1]; Print[cp]; n = n + 1; npd = npd*Prime[n]]

A103782 a(n) = minimal m >= 0 that makes primorial P(n)*2^m-1 prime.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 1, 2, 3, 12, 1, 0, 22, 2, 4, 13, 12, 6, 1, 4, 1, 4, 0, 2, 9, 5, 6, 2, 1, 9, 17, 22, 7, 19, 73, 23, 12, 5, 27, 33, 64, 33, 5, 7, 41, 44, 35, 29, 3, 19, 6, 26, 5, 11, 9, 33, 34, 16, 63, 46, 8, 4, 24, 48, 0, 11, 0, 26, 6, 25, 17, 31, 6, 46, 33, 46, 17, 8, 61, 12, 23, 76, 20, 17
Offset: 2

Views

Author

Lei Zhou, Feb 15 2005

Keywords

Comments

The values of n in A103515

Examples

			P(2)*2^0-1=5 is prime, so a(2)=0; P(9)*2^2-1=892371479 is prime, so a(9)=2;

Crossrefs

Cf. A002110, A005234, A014545, A018239, A006794, A057704, A057705, A103513, A103515.

Programs

  • Mathematica
    nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tn = 0; tt = 1; cp = npd*tt - 1; While[(cp > 1) && (! (PrimeQ[cp])), tn = tn + 1; tt = tt*2; cp = npd*tt - 1]; Print[tn]; n = n + 1; npd = npd*Prime[n]]

A103784 Minimal n that makes primorial P(k)*n-1 prime, k>=2, n>0.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 2, 3, 6, 3, 2, 1, 18, 3, 7, 13, 11, 24, 2, 13, 2, 16, 1, 4, 29, 6, 18, 4, 2, 11, 14, 13, 38, 13, 14, 9, 17, 12, 13, 10, 31, 19, 5, 58, 5, 15, 22, 18, 8, 5, 11, 27, 24, 13, 10, 11, 3, 36, 18, 19, 13, 16, 12, 3, 1, 53, 1, 11, 19, 15, 81, 14, 28, 7, 5, 57, 40, 40, 46, 6, 10
Offset: 2

Views

Author

Lei Zhou, Feb 15 2005

Keywords

Comments

Minimal n of sequence A103783. Weak conjecture: sequence is defined for all k>=2; strong conjecture: a(k)<=(prime(k))^2;

Examples

			P(2)*1-1=5 is prime, so a(2)=1;
P(9)*3-1=669278609 is prime, so a(9)=3;

Crossrefs

Cf. A002110, A103515, A103783.

Programs

  • Mathematica
    nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[(tt <= (Prime[n])^2) && (! (PrimeQ[cp])), tt = tt + 1; cp = npd*tt - 1]; If[tt >= (Prime[n])^2, cp = -cp; tn1 = -tt, tn1 = tt]; Print[tn1]; n = n + 1; npd = npd*Prime[n]]
Showing 1-3 of 3 results.

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