A244952 -id:A244952 - cp's OEIS frontend

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

M. F. Hasler, Jul 13 2014

nonn

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, ...

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

Cf. A002145.

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

A245205 Indices of records in A245203 (= least k>=0 such that 4n+3 is the mean of primes 4(n-k)+3 and 4(n+k)+3).

Original entry on oeis.org

0, 3, 8, 21, 24, 35, 64, 75, 87, 97, 176, 274, 278, 304, 736, 757, 902, 920, 1139, 1936, 4361, 6374, 10181, 11848, 17771, 43487, 49987, 71552, 93124, 152446, 217835, 217856, 243706, 440152, 480487, 864901

Offset: 1

M. F. Hasler, Jul 13 2014

nonn

See A244952 for the record values A244952(n) = A245203(a(n)).

cp's OEIS Frontend

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.

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A245205 Indices of records in A245203 (= least k>=0 such that 4n+3 is the mean of primes 4(n-k)+3 and 4(n+k)+3).

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