A273597 min { x >= 0 | A273595(n) + prime(n)*x + x^2 is composite }, where A273595(n) is such that this is a local maximum.

39, 38, 37, 35, 34, 32, 31, 29, 26, 25, 22, 20, 19, 17, 14, 12, 11, 12, 12, 12, 12, 16, 15, 12, 12, 13, 14, 13, 13, 14, 13, 13, 13, 13, 14, 14, 14, 16, 16, 16, 15, 15, 16, 16, 17

Offset

2,1

Comments

See A273595 for further information and (cross)references.

From the initial values, the sequence seems strictly decreasing, with a(n+1) - a(n) = (prime(n+1) - prime(n))/2; however, this property does not persist beyond n = 16.

This is the subsequence of A273770 with indices n corresponding to odd primes 2n+1, see formula. - M. F. Hasler, Feb 17 2020

Links

Table of n, a(n) for n=2..46.

Index to entries related to primes produced by polynomials.

Formula

a(n) = (81 - prime(n))/2 for 1 < n < 17.

a(n) = A273770((prime(n) - 1)/2). - M. F. Hasler, Feb 17 2020

Prog

(PARI) A273597(n)=A273770(prime(n)\2) \\ changed Feb 17 2020
(PARI) A273597(n, p=prime(n), q=A273756(p\2))={for(x=1, oo, isprime(q+p*x+x^2)||return(x))} \\ M. F. Hasler, Feb 17 2020

Crossrefs

Cf. A002837, A007634, A005846, A097823, A144051, A187057 .. A187060, A190800, A191456 ff.

Sequence in context: A317388 A088344 A268856 * A022995 A023481 A291517

Adjacent sequences: A273594 A273595 A273596 * A273598 A273599 A273600

Keyword

nonn

Author

M. F. Hasler, May 26 2016

Extensions

Edited and extended using A273756(0..100) due to Don Reble, by M. F. Hasler, Feb 17 2020

Status

approved