A141585 Primes of the form (n-(p(n+2)-p(n))/(p(n+1)-p(n-1)))/2, where p(n)=n-th prime.

2, 3, 13, 29, 31, 37, 67, 71, 73, 139, 149, 197, 227, 229, 233, 241, 277, 331, 347, 431, 439, 467, 521, 547, 571, 587, 593, 743, 787, 797, 827, 859, 863, 877, 967, 1031, 1033, 1109, 1129, 1153, 1181, 1277, 1283, 1297, 1439, 1451, 1453, 1523, 1571, 1583, 1693

Offset

1,1

Links

Table of n, a(n) for n=1..51.

Example

If n=5, then
(5-(p(5+2)-p(5))/(p(5+1)-p(5-1)))/2=(5-(17-11)/(13-7))/2=2=a(1).
If n=7, then
(7-(p(7+2)-p(7))/(p(7+1)-p(7-1)))/2=(7-(23-17)/(19-13))/2=3=a(2).
If n=48, then
(48-(p(48+2)-p(48))/(p(48+1)-p(48-1)))/2=(48-(233-227)/(229-223))/2=23=a(3).
If n=695, then
(695-(p(695+2)-p(695))/(p(695+1)-p(695-1)))/2=(695-(5237-5231)/(5233-5227))/2=347=a(4).

Crossrefs

Cf. A000040.

Sequence in context: A191063 A105891 A228991 * A191021 A106867 A141861

Adjacent sequences: A141582 A141583 A141584 * A141586 A141587 A141588

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 10 2008

Extensions

Extended to 51 terms. First omission was 13 = (27 - (109 - 103) / (107 - 101)) / 2. a(3) was incorrect; the 48th prime is 223. Reikku Kulon, Sep 16 2008

Status

approved