cp's OEIS Frontend

A259560 Primes p such that p = 2kq + 1 for k a positive integer, q an odd prime and 2k <= q - 3.

%I A259560 #23 Jul 29 2015 05:47:46
%S A259560 11,23,29,47,53,59,67,79,83,89,103,107,131,137,139,149,167,173,179,
%T A259560 191,223,227,229,233,239,263,269,277,283,293,311,317,347,349,359,367,
%U A259560 373,383,389,431,439,461,467,479,499,503,509,523,557,563,569,587,593,607
%N A259560 Primes p such that p = 2kq + 1 for k a positive integer, q an odd prime and 2k <= q - 3.
%C A259560 This sequence is associated with the conjecture in A245664 that p + q is prime-partitionable.
%C A259560 There are 138438 values of p in the first 216816 primes, i.e., 63.85%, all of which are distinct.
%H A259560 Christopher Hunt Gribble, <a href="/A259560/b259560.txt">Table of n, a(n) for n = 1..20000</a>
%e A259560 The table lists values of n, q, 2k and p for 1 <= n <= 20.
%e A259560 .n      q     2k      p (a(n))
%e A259560 .1      5      2     11
%e A259560 .2     11      2     23
%e A259560 .3      7      4     29
%e A259560 .4     23      2     47
%e A259560 .5     13      4     53
%e A259560 .6     29      2     59
%e A259560 .7     11      6     67
%e A259560 .8     13      6     79
%e A259560 .9     41      2     83
%e A259560 10     11      8     89
%e A259560 11     17      6    103
%e A259560 12     53      2    107
%e A259560 13     13     10    131
%e A259560 14     17      8    137
%e A259560 15     23      6    139
%e A259560 16     37      4    149
%e A259560 17     83      2    167
%e A259560 18     43      4    173
%e A259560 19     89      2    179
%e A259560 20     19     10    191
%p A259560 ppgen := proc (n)
%p A259560   local i, j, k, nprimes, p1a, p1b, p1b_ind, pless, pless_idx, p1b_ind_num_0, p1b_ind_num_1;
%p A259560   pless := {};
%p A259560   for i from 3 to n do
%p A259560     if isprime(i) then
%p A259560       pless := `union`(pless, {i})
%p A259560     end if
%p A259560   end do;
%p A259560   nprimes := numelems(pless);
%p A259560   p1b_ind := Vector(nprimes);
%p A259560   for j to nprimes do
%p A259560     p1a := pless[j];
%p A259560     if (1/2)*pless[-1]+1/2 < p1a then
%p A259560       break
%p A259560     end if;
%p A259560     for k to (1/2)*p1a-3/2 do
%p A259560       p1b := 2*k*p1a+1;
%p A259560       if member(p1b, pless, 'pless_idx') then
%p A259560         p1b_ind[pless_idx] := 1
%p A259560       elif pless[-1] < p1b then
%p A259560         break
%p A259560       end if
%p A259560     end do
%p A259560   end do;
%p A259560   p1b_ind_num_0 := 1;
%p A259560   p1b_ind_num_1 := 0;
%p A259560   for i to nprimes do
%p A259560     if p1b_ind[i] = 0 then
%p A259560       p1b_ind_num_0 := p1b_ind_num_0+1
%p A259560     else
%p A259560       p1b_ind_num_1 := p1b_ind_num_1+1;
%p A259560       fprintf(fop, "%d %d\n", p1b_ind_num_1, pless[i])
%p A259560     end if
%p A259560   end do
%p A259560 end proc;
%p A259560 n := 376200;
%p A259560 ppgen(n);
%o A259560 (PARI) is(n)=my(f=factor(n\2)[,1]); for(i=1,#f, if(n\2/f[i]*2<=f[i]-3, return(isprime(n)))); 0 \\ _Charles R Greathouse IV_, Jul 15 2015
%Y A259560 Cf. A059756, A245664.
%K A259560 nonn
%O A259560 1,1
%A A259560 _Christopher Hunt Gribble_, Jun 30 2015