Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Sep 08 2022 08:46:24
%S 3565931,3653863,3985903,5425613,5647361,6126971,6292081,6532553,
%T 7133983,7360363,7389493,7700131,7865833,7956163,8467903,8708291,
%U 8972701,9203743,9603361,9863551,10279813,10971743,11998391,12225251,12474251,12620843,12966881,13288211,13376261,13543451
%N First of three consecutive primes with common gap 48.
%H OEIS Wiki, <a href="/wiki/Consecutive_primes_in_arithmetic_progression#CPAP_with_given_gap">Consecutive primes in arithmetic progression</a>, updated Jan. 2020.
%t Select[Partition[Prime[Range[900000]],3,1],Differences[#]=={48,48}&] [[All,1]] (* _Harvey P. Dale_, Aug 23 2021 *)
%o (PARI) vecextract( A134123, select(t->t==48, A134123[^1]-A134123[^-1], 1)) \\ Terms of A134123 with indices corresponding to first differences of 48: gives a(1..56) from A134123(1..10^4).
%o (Magma) [p:p in PrimesUpTo(14000000)| NextPrime(p)-p eq 48 and NextPrime(p+48)-p eq 96]; // _Marius A. Burtea_, Jan 03 2020
%Y Cf. A134123, A067388: first of two, resp. four primes with common gap 48.
%Y Cf. A047948, A052188, A052189, A052190, A052195, A052197, A052198, A089234 (analog for gaps 2, 4, 6, 12, 18, 24, ..., 60).
%K nonn
%O 1,1
%A _M. F. Hasler_, Jan 02 2020