A062252 -id:A062252 - cp's OEIS frontend

A060424 Record-setting n's for the function q(n), the minimum prime q such that n(q+1)-1 is prime p (i.e., q(n) > q(j) for all 0 < j < n).

1, 3, 7, 13, 31, 51, 101, 146, 311, 1332, 2213, 6089, 10382, 11333, 32003, 83633, 143822, 176192, 246314, 386237, 450644, 1198748, 2302457, 5513867, 9108629, 11814707, 16881479, 18786623, 24911213, 28836722, 34257764, 196457309

Offset: 1

Matthew Conroy, Apr 10 2001

nonn

			a(3)=7, since q(7)=5 and q(j) < 5 for 0 < j < 7.

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. See A062252 and A062256 for the corresponding values of q and p.

q[n_] := Module[{p = 2}, While[! PrimeQ[n*(p+1)-1], p = NextPrime[p]]; p]; record = 0; a[0] = 0; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, If[q[k] > record, record = q[k]; Print[k]; Return[k]]]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Nov 18 2013 *)

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

cp's OEIS Frontend

A060424 Record-setting n's for the function q(n), the minimum prime q such that n(q+1)-1 is prime p (i.e., q(n) > q(j) for all 0 < j < n).

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