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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. 8

%I

%S 2,5,11,11,19,17,41,23,53,29,43,47,103,41,59,47,67,53,113,59,83,131,

%T 137,71,149,103,107,83,173,89,433,127,131,101,139,107,443,113,233,239,

%U 163,167,257,131,179,137,281,191,293,149,1019,311,211,431,439,167,227

%N 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.

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

%H T. D. Noe, <a href="/A062251/b062251.txt">Table of n, a(n) for n = 1..10000</a>

%H Matthew M. Conroy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL4/CONROY/conroy.html">A sequence related to a conjecture of Schinzel</a>, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.

%H Peter Luschny, <a href="/wiki/User:Peter_Luschny/SchinzelSierpinskiConjectureAndCalkinWilfTree"> Schinzel-Sierpinski conjecture and Calkin-Wilf tree.</a>

%H A. Schinzel and W. Sierpiński, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa4/aa432.pdf">Sur certaines hypothèses concernant les nombres premiers</a>, Acta Arithmetica 4 (1958), 185-208; erratum 5 (1958) p. 259.

%F a(n) = (A060324(n) + 1) * n - 1. - _Reinhard Zumkeller_, Aug 28 2014

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

%p a:= proc(n) local q;

%p q:= 2;

%p while not isprime(n*(q+1)-1) do

%p q:= nextprime(q);

%p od; n*(q+1)-1

%p end:

%p seq(a(n), n=1..300);

%t 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 *)

%o (Haskell)

%o a062251 n = (a060324 n + 1) * n - 1 -- _Reinhard Zumkeller_, Aug 28 2014

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

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_, Jul 01 2001

%E More terms from _Vladeta Jovovic_, Jul 02 2001

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Last modified March 20 19:23 EDT 2019. Contains 321349 sequences. (Running on oeis4.)