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 A259560 Primes p such that p = 2kq + 1 for k a positive integer, q an odd prime and 2k <= q - 3. 1
 11, 23, 29, 47, 53, 59, 67, 79, 83, 89, 103, 107, 131, 137, 139, 149, 167, 173, 179, 191, 223, 227, 229, 233, 239, 263, 269, 277, 283, 293, 311, 317, 347, 349, 359, 367, 373, 383, 389, 431, 439, 461, 467, 479, 499, 503, 509, 523, 557, 563, 569, 587, 593, 607 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is associated with the conjecture in A245664 that p + q is prime-partitionable. There are 138438 values of p in the first 216816 primes, i.e., 63.85%, all of which are distinct. LINKS Christopher Hunt Gribble, Table of n, a(n) for n = 1..20000 EXAMPLE The table lists values of n, q, 2k and p for 1 <= n <= 20. .n q 2k p (a(n)) .1 5 2 11 .2 11 2 23 .3 7 4 29 .4 23 2 47 .5 13 4 53 .6 29 2 59 .7 11 6 67 .8 13 6 79 .9 41 2 83 10 11 8 89 11 17 6 103 12 53 2 107 13 13 10 131 14 17 8 137 15 23 6 139 16 37 4 149 17 83 2 167 18 43 4 173 19 89 2 179 20 19 10 191 MAPLE ppgen := proc (n) local i, j, k, nprimes, p1a, p1b, p1b_ind, pless, pless_idx, p1b_ind_num_0, p1b_ind_num_1; pless := {}; for i from 3 to n do if isprime(i) then pless := `union`(pless, {i}) end if end do; nprimes := numelems(pless); p1b_ind := Vector(nprimes); for j to nprimes do p1a := pless[j]; if (1/2)*pless[-1]+1/2 < p1a then break end if; for k to (1/2)*p1a-3/2 do p1b := 2*k*p1a+1; if member(p1b, pless, 'pless_idx') then p1b_ind[pless_idx] := 1 elif pless[-1] < p1b then break end if end do end do; p1b_ind_num_0 := 1; p1b_ind_num_1 := 0; for i to nprimes do if p1b_ind[i] = 0 then p1b_ind_num_0 := p1b_ind_num_0+1 else p1b_ind_num_1 := p1b_ind_num_1+1; fprintf(fop, "%d %d\n", p1b_ind_num_1, pless[i]) end if end do end proc; n := 376200; ppgen(n); PROG (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 CROSSREFS Cf. A059756, A245664. Sequence in context: A105898 A247228 A243461 * A136001 A158203 A161754 Adjacent sequences: A259557 A259558 A259559 * A259561 A259562 A259563 KEYWORD nonn AUTHOR Christopher Hunt Gribble, Jun 30 2015 STATUS approved

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Last modified September 26 04:29 EDT 2023. Contains 365653 sequences. (Running on oeis4.)