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A049500 Smallest prime p such that p + 4^k is also prime for all k = 1, ..., n. 5
3, 3, 3, 7, 7, 37, 37, 163, 671353, 13243063, 5906322013, 12087247687 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)