A178668 Maximal prime divisor of the average of the twin prime pairs, different from 2 and 3. In case of maximal prime divisor is 2 or 3, then a(n)=1.

1, 1, 1, 1, 5, 7, 5, 1, 17, 1, 23, 5, 5, 1, 11, 19, 5, 5, 47, 13, 29, 7, 1, 11, 29, 19, 5, 103, 107, 11, 5, 137, 23, 13, 7, 17, 43, 7, 59, 13, 1, 41, 71, 43, 31, 11, 17, 11, 19, 31, 67, 5, 139, 283, 41, 149, 13, 313, 23, 13, 37, 13, 347, 29, 11, 71, 17, 373, 7, 11, 13, 397, 17, 1, 443, 7, 113, 13, 31, 467, 11, 5, 13, 11, 271, 181, 11, 37, 7, 281, 113, 577, 17, 7, 59, 593, 199, 17, 157, 13

Offset: 1

Author

Vladimir Shevelev, Dec 25 2010

Keywords

• nonn

Comments

78 from the first 100 terms are first or second members of twin pairs and only 12 are not. In a natural supposition that for large prime terms the latter should be in the majority, there are reasons to assume that the number N for which it occurs for the first time is very large.

The average of a twin-prime pair is the same as 1 + the lower twin prime, whose largest prime factor is tabulated in A060210.

Crossrefs

Cf. A178456, A178527, A001359

Programs

Mathematica

s = Plus @@@ Select[ Partition[ Prime@ Range@ 350, 2, 1], #[[1]] + 2 == #[[2]] &]; f[n_] := Max[First /@ FactorInteger@ n] /. {2 -> 1, 3 -> 1}, f /@ s