A057221 Numbers k such that 2^k + 19 is prime.

2, 6, 30, 162, 654, 714, 1370, 1662, 1722, 2810, 77142, 156254, 432974, 1092242, 1245230

Offset: 1

Author

Robert G. Wilson v, Sep 17 2000

Keywords

• nonn
• more
• hard

Comments

a(14) > 5*10^5. - Robert Price, Aug 27 2015

All terms are even. - Robert Israel, Aug 28 2015

For numbers k in this sequence, the number 2^(k-1)*(2^k+19) has deficiency 20 (see A223607). - M. F. Hasler, Jul 18 2016

Links

• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 2^n+19, PRP Top Records.

Crossrefs

Cf. A223607, A253774.

Cf. A019434 (primes 2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), A057196(2^k+9), A102633 (2^k+11), A102634 (2^k+13), A057197 (2^k+15), A057200 (2^k+17), this sequence (2^k+19), A057201 (2^k+21), A057203 (2^k+23).

Programs

Magma

[n: n in [0..1000] | IsPrime(2^n+19)]; // Vincenzo Librandi, Aug 28 2015

Maple

select(n -> isprime(2^n+19), [seq(2*i,i=1..10000)]); # Robert Israel, Aug 28 2015

Mathematica

Do[ If[ PrimeQ[ 2^n + 19 ], Print[ n ] ], {n, 1, 15000} ]
Select[Range[10000], PrimeQ[2^# + 19] &] (* Vincenzo Librandi, Aug 28 2015 *)

PARI

for(n=1,oo,ispseudoprime(2^n+19)&&print1(n",")) \\ M. F. Hasler, Jul 18 2016

Formula

a(n) = 2*A253774(n). - Joerg Arndt, Aug 28 2015

Extensions

a(11)-a(13) from Robert Price, Aug 27 2015

Edited by M. F. Hasler, Jul 18 2016

a(14)-a(15) found by Stefano Morozzi, added by Elmo R. Oliveira, Nov 19 2023