A239727 Numbers n such that the least prime of the form 2nk + 1 has a value of k that is larger than the k values for all smaller n.

1, 4, 12, 19, 59, 92, 159, 227, 256, 514, 706, 1466, 5207, 21209, 62809, 86914, 152351, 170167, 321472, 424783, 491702, 860831, 1415551, 1581442, 2679809, 4691576, 6238447, 6630812, 17886697, 27507569, 30581429, 57868997, 108830332, 116156102, 127813579, 154641337, 1072567492, 1101795593, 3546087418, 10371779744

Offset: 1

Author

Charles R Greathouse IV, Mar 25 2014

Keywords

• nonn

Comments

RECORDS transform of A016014.

Sequence is infinite; a terrible upper bound can be derived from Linnik's theorem together with the Chinese Remainder Theorem, giving a(n) << exp(a(n-1)^6).

Examples

			2*4*2+1 = 17 is prime with k = 2, but 1 through 3 have k = 1.
2*12*3+1 = 73 is prime with k = 3, but k = 2 for 4, 7, 10 and k = 1 for the other n < 12.
		

Crossrefs

Cf. A016014, A239746.

Programs

PARI

A016014(n)=my(k); while(!isprime(2*n*k+++1),);k
r=0;for(n=1,1e8,t=A016014(n);if(t>r,r=t;print1(n", ")))

Formula

A016014(a(n)) = A239746(n). - Zak Seidov, Mar 27 2014

Extensions

a(37)-a(40) from Giovanni Resta, Mar 26 2014