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

1,2

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).

Links

Table of n, a(n) for n=1..40.

Formula

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

Example

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.

Prog

(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", ")))

Crossrefs

Cf. A016014, A239746.

Sequence in context: A304474 A301068 A169583 * A341888 A009557 A240762

Adjacent sequences: A239724 A239725 A239726 * A239728 A239729 A239730

Keyword

nonn

Author

Charles R Greathouse IV, Mar 25 2014

Extensions

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

Status

approved