A049500 Smallest prime p such that p + 4^k is also prime for all k = 1, ..., n.

3, 3, 3, 7, 7, 37, 37, 163, 671353, 13243063, 5906322013, 12087247687

Offset

1,1

Comments

a(13) > 10^11. - Donovan Johnson, Dec 02 2009

Links

Table of n, a(n) for n=1..12.

Example

Prime 3 generates the {3,7,19,67} exponential prime-chain of length 4 if the start is also counted.
The smallest "exponential 11-chain" starts with 13243063 as follows: 13243063, 13243067, 13243079, 13243127, 13243319, 13244087, 13247159, 13259447, 13308599, 13505207, 14291639.

Mathematica

Table[p = 2; While[Times @@ Boole@ PrimeQ[p + 4^Range@ n] != 1, p = NextPrime@ p]; p, {n, 10}] (* Michael De Vlieger, Mar 05 2017 *)

Prog

(PARI) okchain(n, p)=for (k=1, n, if (! isprime(p + 4^k), return (0)); ); return (1);
a(n) = {p = 2; while (! okchain(n, p), p = nextprime(p+1)); p; } \\ Michel Marcus, Dec 17 2013

Crossrefs

Cf. A023200, A049492-A049499.

Sequence in context: A132197 A077885 A031503 * A227826 A268127 A200076

Adjacent sequences: A049497 A049498 A049499 * A049501 A049502 A049503

Keyword

nonn,more

Author

Labos Elemer

Extensions

a(11)-a(12) from Donovan Johnson, Dec 02 2009

Status

approved