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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.

%I A062251 #39 Nov 20 2017 03:31:12
%S A062251 2,5,11,11,19,17,41,23,53,29,43,47,103,41,59,47,67,53,113,59,83,131,
%T A062251 137,71,149,103,107,83,173,89,433,127,131,101,139,107,443,113,233,239,
%U A062251 163,167,257,131,179,137,281,191,293,149,1019,311,211,431,439,167,227
%N 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.
%C A062251 A conjecture of Schinzel, if true, would imply that such a p always exists.
%H A062251 T. D. Noe, <a href="/A062251/b062251.txt">Table of n, a(n) for n = 1..10000</a>
%H A062251 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 A062251 Peter Luschny, <a href="/wiki/User:Peter_Luschny/SchinzelSierpinskiConjectureAndCalkinWilfTree"> Schinzel-Sierpinski conjecture and Calkin-Wilf tree.</a>
%H A062251 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 A062251 a(n) = (A060324(n) + 1) * n - 1. - _Reinhard Zumkeller_, Aug 28 2014
%e A062251 1 = (2+1)/(2+1), 2 = (5+1)/(2+1), 3 = (11+1)/(3+1), 4 = (11+1)/(2+1), ...
%p A062251 a:= proc(n) local q;
%p A062251        q:= 2;
%p A062251        while not isprime(n*(q+1)-1) do
%p A062251           q:= nextprime(q);
%p A062251        od; n*(q+1)-1
%p A062251     end:
%p A062251 seq(a(n), n=1..300);
%t A062251 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 A062251 (Haskell)
%o A062251 a062251 n = (a060324 n + 1) * n - 1 -- _Reinhard Zumkeller_, Aug 28 2014
%Y A062251 Cf. A060424. Values of q are given in A060324.
%K A062251 nonn,nice,easy
%O A062251 1,1
%A A062251 _N. J. A. Sloane_, Jul 01 2001
%E A062251 More terms from _Vladeta Jovovic_, Jul 02 2001