A100021 -id:A100021 - cp's OEIS frontend

A099389 Subsequence of primes in sequence b(n) = 3*prime(n) - prime(n+1) - 3 (A100021).

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

Offset: 1

Giovanni Teofilatto, Nov 17 2004

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

Cf. A100021, A099382.

Select[3#[[1]]-#[[2]]-3&/@Partition[Prime[Range[100]],2,1],PrimeQ] (* Harvey P. Dale, Oct 13 2018 *)

for(n=1,91,if(isprime(k=3*prime(n)-prime(n+1)-3),print1(k,",")))

Edited and extended by Klaus Brockhaus, Nov 19 2004

A098764 a(n) = 3p - q where p and q are consecutive primes.

Original entry on oeis.org

3, 4, 8, 10, 20, 22, 32, 34, 40, 56, 56, 70, 80, 82, 88, 100, 116, 116, 130, 140, 140, 154, 160, 170, 190, 200, 202, 212, 214, 212, 250, 256, 272, 268, 296, 296, 308, 322, 328, 340, 356, 352, 380, 382, 392, 386, 410, 442, 452, 454, 460, 476, 472, 496, 508, 520

Offset: 1

Giovanni Teofilatto, Sep 30 2004

Except for the initial term, a(n)=={2, 4} mod 6.

Not monotonic: a(29) = 214 > 212 = a(30), a(33) = 272 > 268 = a(34), etc. - Charles R Greathouse IV, Jun 03 2013

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A000040, A001043, A001223, A001748, A047235, A100021.

ListConvolve[{-1,3},Prime[Range[100]]] (* Paolo Xausa, Nov 02 2023 *)

a(n) = 3*prime(n) - prime(n+1) \\ Michel Marcus, Jun 03 2013

a(n) = A001043(n) - 2*A001223(n).
a(n) = 3*A000040(n)-A000040(n+1) = A001748(n)-A000040(n+1) = A001747(n+1)-A001223(n). - R. J. Mathar, Apr 22 2010
a(n) ~ 2n log n. - Charles R Greathouse IV, Jun 03 2013
a(n) = A100021(n) + 3. - Hugo Pfoertner, Nov 02 2023
a(n) = A062234(n) + A000040(n). - Anthony S. Wright, Feb 19 2024

Corrected (116 duplicated) by R. J. Mathar, Apr 22 2010

cp's OEIS Frontend

A099389 Subsequence of primes in sequence b(n) = 3*prime(n) - prime(n+1) - 3 (A100021).

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