A099389 -id:A099389 - cp's OEIS frontend

A099382 Primes of the form 3p - q - 3, where p and q are consecutive primes.

5, 7, 17, 19, 29, 31, 37, 53, 67, 79, 97, 113, 127, 137, 151, 157, 167, 197, 199, 211, 269, 293, 337, 349, 353, 379, 383, 389, 439, 449, 457, 547, 557, 569, 607, 617, 619, 653, 661, 691, 751, 757, 787, 829, 857, 877, 887, 907, 919, 947

Offset: 1

Giovanni Teofilatto, Nov 17 2004

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A099389.

v=List(); p=2; forprime(q=3,1e6, if(isprime(t=3*p-q-3), listput(v,t)); p=q); v=vecsort(Vec(v),,8)

Edited and extended by Klaus Brockhaus, Nov 19 2004

Terms corrected by Charles R Greathouse IV, Feb 15 2011

A100021 a(n) = 3*prime(n) - prime(n+1) - 3.

Original entry on oeis.org

0, 1, 5, 7, 17, 19, 29, 31, 37, 53, 53, 67, 77, 79, 85, 97, 113, 113, 127, 137, 137, 151, 157, 167, 187, 197, 199, 209, 211, 209, 247, 253, 269, 265, 293, 293, 305, 319, 325, 337, 353, 349, 377, 379, 389, 383, 407, 439, 449, 451, 457, 473, 469, 493, 505, 517, 533, 533, 547

Offset: 1

Giovanni Teofilatto, Nov 20 2004

Except for the initial term, a(n)==(1,5) mod 6.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A099389 for the primes arising in the sequence, A098764.

Maple
```
f:=n->3*ithprime(n)-ithprime(n+1)-3;
```

3#[[1]]-#[[2]]-3&/@Partition[Prime[Range[80]],2,1] (* Harvey P. Dale, Oct 13 2018 *)

a(n) = 3*prime(n) - prime(n+1) - 3; \\ Michel Marcus, Jan 31 2023

a(n) = A098764(n) - 3.

Corrected by Neven Juric (neven.juric(AT)apis-it.hr), rechecked by N. J. A. Sloane, Jun 13 2006

cp's OEIS Frontend

A099382 Primes of the form 3p - q - 3, where p and q are consecutive primes.

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A100021 a(n) = 3*prime(n) - prime(n+1) - 3.

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