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

Author

M. F. Hasler, May 26 2016

Keywords

• nonn

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

• Index to entries related to primes produced by polynomials.

Crossrefs

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

Programs

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

Formula

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

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

Extensions

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