A157979 Least nonnegative k such that 3^(2^n)+k is prime.

0, 2, 2, 2, 26, 70, 92, 190, 788, 436, 86, 3032, 13622, 2810, 7562, 33172, 16942

Offset

0,2

Comments

The associated primes are in A157980.

All 3^(2^n)+a(n) = A157980(n) for n <= 11 are certified primes. - D. S. McNeil, Mar 15 2009

Links

Table of n, a(n) for n=0..16.

Florentin Smarandache, Seven Conjectures in Geometry and Number Theory, arXiv:0903.1380 [math.GM], Mar 8, 2009.

Formula

a(n) = Min{k>=0 such that 3^(2^n)+k is prime} = Min{k>=0 such that A000244(A000079(n))+k is in A000040}.

Example

a(0) = 0 because 3^2^0 + 0 = 3^1 + 0 = 3 is prime. a(1) = 2 because 3^2^1 + 2 = 3^2 + 0 = 3 is prime. a(2) = 2 because 3^4 + 2 = 83 is prime. a(3) = 2 because 3^8 + 2 = 6563 is prime. a(4) = 26 because 3^16 + 26 = 43046747 is prime. a(5) = 70 because 3^32 + 2 = 1853020188851911 is prime. a(6) = 92 because 3^64 + 2 = 3433683820292512484657849089373 is prime.

Mathematica

lnnk[n_]:=With[{c=3^(2^n)}, NextPrime[c]-c]; Join[{0}, Array[lnnk, 10]] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Nov 02 2024 *)

Prog

(PARI) { a(n) = nextprime( 3^(2^n) ) - 3^(2^n) } \\ Max Alekseyev, Sep 13 2009

Crossrefs

Cf. A000040, A000079, A000244, A000215, A157980.

Sequence in context: A153438 A098915 A095855 * A147975 A083148 A368204

Adjacent sequences: A157976 A157977 A157978 * A157980 A157981 A157982

Keyword

more,nonn,hard

Author

Jonathan Vos Post, Mar 10 2009

Extensions

a(7)-a(11) from D. S. McNeil, Mar 15 2009

a(12)-a(14) from Max Alekseyev, Sep 13 2009

a(15)-a(16) from Donovan Johnson, Jul 11 2010

Status

approved