A060424 -id:A060424 - cp's OEIS frontend

A060324 a(n) is the minimal prime q such that n*(q+1)-1 is prime, that is, the smallest prime q so that n = (p+1)/(q+1) with p prime; or a(n) = -1 if no such q exists.

2, 2, 3, 2, 3, 2, 5, 2, 5, 2, 3, 3, 7, 2, 3, 2, 3, 2, 5, 2, 3, 5, 5, 2, 5, 3, 3, 2, 5, 2, 13, 3, 3, 2, 3, 2, 11, 2, 5, 5, 3, 3, 5, 2, 3, 2, 5, 3, 5, 2, 19, 5, 3, 7, 7, 2, 3, 2, 5, 2, 7, 11, 3, 2, 5, 2, 5, 3, 11, 5, 3, 5, 13, 5, 5, 2, 3, 2, 7, 2, 7, 5, 3, 2, 5, 2, 3, 2, 17, 2, 7, 3, 5, 2, 3, 3, 11, 2, 5, 5

Offset: 1

Matthew Conroy, Mar 29 2001

A conjecture of Schinzel, if true, would imply that such a q always exists.

			1 = (2+1)/(2+1), so the first term is 2; 3(2+1) - 1 = 8 which is not prime, yet 3(3+1) - 1 = 11 is prime (3 = (11+1)/(3+1)) so the 3rd term is 3.

T. D. Noe, Table of n, a(n) for n = 1..10000
Matthew M. Conroy, A sequence related to a conjecture of Schinzel, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.
Peter Luschny, Schinzel-Sierpinski conjecture and Calkin-Wilf tree.

Cf. A060424. Values of p are given in A062251.

Cf. A000040, A010051.

a060324 n = head [q | q <- a000040_list, a010051' (n * (q + 1) - 1) == 1]
-- Reinhard Zumkeller, Aug 28 2014

a:= proc(n) local q;
       q:= 2;
       while not isprime(n*(q+1)-1) do
          q:= nextprime(q);
       od; q
    end:
seq(a(n), n=1..300); # Alois P. Heinz, Feb 11 2011

a[n_] := (q = 2; While[!PrimeQ[n*(q + 1) - 1], q = NextPrime[q]]; q); a /@ Range[100] (* Jean-François Alcover, Jul 20 2011, after Maple prog. *)

a(n) = {my(q=2); while (!isprime(n*(q+1)-1), q = nextprime(q+1)); q;} \\ Michel Marcus, Nov 20 2017

a(n) = (A062251(n)+1) / n - 1. - Reinhard Zumkeller, Aug 28 2014

A062251 Take minimal prime q such that n(q+1)-1 is prime (A060324), that is, the smallest prime q so that n = (p+1)/(q+1) with p prime; sequence gives values of p.

Original entry on oeis.org

2, 5, 11, 11, 19, 17, 41, 23, 53, 29, 43, 47, 103, 41, 59, 47, 67, 53, 113, 59, 83, 131, 137, 71, 149, 103, 107, 83, 173, 89, 433, 127, 131, 101, 139, 107, 443, 113, 233, 239, 163, 167, 257, 131, 179, 137, 281, 191, 293, 149, 1019, 311, 211, 431, 439, 167, 227

Offset: 1

N. J. A. Sloane, Jul 01 2001

A conjecture of Schinzel, if true, would imply that such a p always exists.

			1 = (2+1)/(2+1), 2 = (5+1)/(2+1), 3 = (11+1)/(3+1), 4 = (11+1)/(2+1), ...

T. D. Noe, Table of n, a(n) for n = 1..10000
Matthew M. Conroy, A sequence related to a conjecture of Schinzel, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.
Peter Luschny, Schinzel-Sierpinski conjecture and Calkin-Wilf tree.
A. Schinzel and W. Sierpiński, Sur certaines hypothèses concernant les nombres premiers, Acta Arithmetica 4 (1958), 185-208; erratum 5 (1958) p. 259.

Cf. A060424. Values of q are given in A060324.

a062251 n = (a060324 n + 1) * n - 1 -- Reinhard Zumkeller, Aug 28 2014

a:= proc(n) local q;
       q:= 2;
       while not isprime(n*(q+1)-1) do
          q:= nextprime(q);
       od; n*(q+1)-1
    end:
seq(a(n), n=1..300);

a[n_] := (q = 2; While[ ! PrimeQ[n*(q+1)-1], q = NextPrime[q]]; n*(q+1)-1); Table[a[n], {n, 1, 57}] (* Jean-François Alcover, Feb 17 2012, after Maple *)

a(n) = (A060324(n) + 1) * n - 1. - Reinhard Zumkeller, Aug 28 2014

More terms from Vladeta Jovovic, Jul 02 2001

A062256 Record-setting values of q(n), the minimal prime q such that n(q+1)-1 is a prime p (i.e., q(n) > q(j) for all 0 < j < n).

Original entry on oeis.org

2, 11, 41, 103, 433, 1019, 2423, 6131, 22391, 146519, 398339, 1461359, 2803139, 3943883, 11329061, 37133051, 72486287, 89857919, 152222051, 247964153, 316352087, 927830951, 2030767073, 5359478723, 8908239161, 11980112897, 17219108579, 20740431791, 27651446429

Offset: 1

N. J. A. Sloane, Jul 01 2001

			31 = (433+1)/(13+1).

Amiram Eldar, Table of n, a(n) for n = 1..39
Matthew M. Conroy, A sequence related to a conjecture of Schinzel, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.

Cf. A060324, A062251. Values of n are in A060424, values of q in A062252.

a(n) = A060424(n)*(A062252(n)+1) - 1.

More terms from Vladeta Jovovic, Jul 02 2001

A062252 Record-setting values of q(n), the minimal prime q such that n(q+1)-1 is a prime p (i.e., q(n) > q(j) for all 0 < j < n).

Original entry on oeis.org

2, 3, 5, 7, 13, 19, 23, 41, 71, 109, 179, 239, 269, 347, 353, 443, 503, 509, 617, 641, 701, 773, 881, 971, 977, 1013, 1019, 1103, 1109, 1223, 1559, 1607, 1709, 1889, 2063, 2297, 2663, 2963, 3137

Offset: 1

N. J. A. Sloane, Jul 01 2001

			31 = (433+1)/(13+1).

Matthew M. Conroy, A sequence related to a conjecture of Schinzel, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.

Cf. A060324, A062251. Values of n are in A060424, values of p in A062256.

a(36)-a(39) from Amiram Eldar, Jan 26 2019

cp's OEIS Frontend

A060324 a(n) is the minimal prime q such that n*(q+1)-1 is prime, that is, the smallest prime q so that n = (p+1)/(q+1) with p prime; or a(n) = -1 if no such q exists.

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A062251 Take minimal prime q such that n(q+1)-1 is prime (A060324), that is, the smallest prime q so that n = (p+1)/(q+1) with p prime; sequence gives values of p.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

Formula

Extensions

A062256 Record-setting values of q(n), the minimal prime q such that n(q+1)-1 is a prime p (i.e., q(n) > q(j) for all 0 < j < n).

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

Extensions

A062252 Record-setting values of q(n), the minimal prime q such that n(q+1)-1 is a prime p (i.e., q(n) > q(j) for all 0 < j < n).

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions