A245203 Least k>=0 such that A004767(n) = 4n+3 is the mean of primes 4(n-k)+3 and 4(n+k)+3; or -1 if no such k exists.

0, 0, 0, 1, 0, 0, 1, 0, 3, 2, 0, 0, 2, 3, 0, 1, 0, 0, 1, 0, 0, 4, 3, 3, 7, 0, 0, 7, 3, 3, 4, 0, 0, 1, 0, 9, 4, 0, 6, 2, 0, 0, 2, 6, 0, 4, 6, 0, 1, 0, 6, 4, 0, 6, 2, 0, 0, 2, 9, 0, 5, 6, 0, 4, 12, 0, 1, 0, 9, 7, 0, 6, 5, 3, 12, 16, 0, 0, 8, 3, 15, 5, 0, 6, 2, 9, 0, 17, 6, 0, 1, 0, 3, 2, 0, 0, 14, 27, 9, 5, 9, 6, 7, 12, 0, 10, 15, 0, 1, 0, 0, 4, 3, 3, 5, 0, 0, 2, 3, 0, 1, 0, 0, 1, 0, 0, 4

Offset: 0

Author

M. F. Hasler, Jul 13 2014

Keywords

• nonn

Comments

It has been conjectured that A004767(n) = 4n+3 is either prime or the mean of two primes in sequence A004767.

See A244952 and A245205 for record values and indices of these records. Some of these records are a(97)=27, a(1139)=120, a(10181)=225, a(93124)=435, a(864901)=894, ...

Links

• M. F. Hasler, Table of n, a(n) for n = 0..9999
• Mike T.W., Could I add this conjecture to A004767: 4*n+3?, SeqFan list, Jul 10 2014

Crossrefs

Cf. A002145.

Programs

PARI

a(n)={-!forstep(k=0,n=4*n+3,4,isprime(n-k)&&isprime(n+k)&&return(k\4))}