A053177 Odd composite k such that (k-1)/2 is prime.

15, 27, 35, 39, 63, 75, 87, 95, 119, 123, 135, 143, 147, 159, 195, 203, 207, 215, 219, 255, 275, 279, 299, 303, 315, 327, 335, 363, 387, 395, 399, 423, 447, 455, 459, 483, 515, 527, 539, 543, 555, 567, 615, 623, 627, 635, 663, 675, 695, 699, 707, 735, 747

Offset: 1

Author

Enoch Haga, Feb 29 2000

Keywords

• easy
• nonn

Comments

Composite numbers produced in A053176.

Examples

			a(3)=35 and 35-1=34, 34/2=17, prime.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• R. P. Boas & N. J. A. Sloane, Correspondence, 1974

Crossrefs

Cf. A053176, A005385, A005382, A259978.

Programs

Mathematica

Select[2 Prime@ Range@ 74 + 1, CompositeQ] (* Michael De Vlieger, Jul 13 2015 *)
Select[Range[1,801,2],CompositeQ[#]&&PrimeQ[(#-1)/2]&] (* Harvey P. Dale, Apr 01 2019 *)

PARI

main(size)={my(v=vector(size),i,t=1);for(i=1, size, while(isprime(2*prime(t)+1), t++); v[i]=2*prime(t)+1;t++;);return(v)} /* Anders Hellström, Jul 13 2015 */

Formula

From the composite, subtract 1, divide by 2 and result is a prime.

Extensions

Definition clarified by Peter Munn, Oct 26 2017