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A072060 Smallest prime p such that 2*p+1 has n prime factors (with multiplicity).

%I A072060 #8 Feb 05 2023 11:03:29
%S A072060 2,7,13,67,283,607,1093,12757,22963,49207,482233,1623847,797161,
%T A072060 14614627,19929037,35872267,150663523,2044719247,1355971711,
%U A072060 9879222469,37773497677,200490103057,172595827849,235357947067,1176789735337,5507375961379,10591107618037
%N A072060 Smallest prime p such that 2*p+1 has n prime factors (with multiplicity).
%H A072060 Daniel Suteu, <a href="/A072060/b072060.txt">Table of n, a(n) for n = 1..500</a>
%e A072060 a(4)=67=A000040(19): 2*67+1 = 135 = 5*3^3, 4 factors.
%o A072060 (PARI)
%o A072060 generate(A, B, n) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p,ceil(A/m)), B\m, my(t=m*q); if(isprime((t-1)/2), listput(list, (t-1)/2))), forprime(q = p, sqrtnint(B\m, n), my(t=m*q); list=concat(list, f(t, q, n-1)))); list); vecsort(Vec(f(1, 3, n)));
%o A072060 a(n) = my(x=2^n, y=2*x); while(1, my(v=generate(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ _Daniel Suteu_, Feb 05 2023
%Y A072060 Cf. A001222, A023595, A072055, A072059.
%K A072060 nonn
%O A072060 1,1
%A A072060 _Reinhard Zumkeller_, Jun 11 2002
%E A072060 More terms from _Don Reble_, Apr 15 2003