A052188 -id:A052188 - cp's OEIS frontend

A329578 First of three consecutive primes with common gap 48.

3565931, 3653863, 3985903, 5425613, 5647361, 6126971, 6292081, 6532553, 7133983, 7360363, 7389493, 7700131, 7865833, 7956163, 8467903, 8708291, 8972701, 9203743, 9603361, 9863551, 10279813, 10971743, 11998391, 12225251, 12474251, 12620843, 12966881, 13288211, 13376261, 13543451

Offset: 1

M. F. Hasler, Jan 02 2020

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
OEIS Wiki, Consecutive primes in arithmetic progression, updated Jan. 2020.

Subsequence of A134123 (first of two primes with common gap 48).
A067388 (first of four primes with common gap 48) is a subsequence.
Cf. A047948, A052188, A052189, A052190, A052195, A052197, A052198, A089234 (analog for gaps 2, 4, 6, 12, 18, 24, ..., 60).

[p:p in PrimesUpTo(14000000)| NextPrime(p)-p eq 48 and NextPrime(p+48)-p eq 96]; // Marius A. Burtea, Jan 03 2020

Select[Partition[Prime[Range[900000]],3,1],Differences[#]=={48,48}&] [[All,1]] (* Harvey P. Dale, Aug 23 2021 *)

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).

A128312 List of triples of primes with common difference 12.

Original entry on oeis.org

199, 211, 223, 1499, 1511, 1523, 4397, 4409, 4421, 4679, 4691, 4703, 7829, 7841, 7853, 9859, 9871, 9883, 11287, 11299, 11311, 11399, 11411, 11423, 11719, 11731, 11743, 12829, 12841, 12853, 15149, 15161, 15173, 16607, 16619, 16631, 17419

Offset: 1

Zerinvary Lajos, May 04 2007

			199, 211, 223
1499, 1511, 1523
4397, 4409, 4421
4679, 4691, 4703
7829, 7841, 7853
9859, 9871, 9883
11287, 11299, 11311
11399, 11411, 11423
etc...

Cf. A052188 (1st column).

for i from 1 by 1 to 4000 do > if ithprime(i+1) = ithprime(i) +12 and ithprime(i+2) = ithprime(i) + 24 then print(ithprime(i),ithprime(i+1),ithprime(i+2)); > fi; > od;#

s={};Do[p=Prime[n];If[NextPrime[p]==p+12&&NextPrime[p,2]==p+24,AppendTo[s,{p,p+12,p+24}]],{n,2100}];Flatten[s] (* James C. McMahon, Jan 07 2025 *)

A374719 Primes p such that p + 48 and p + 96 are also prime.

Original entry on oeis.org

5, 11, 13, 31, 41, 53, 61, 83, 101, 103, 131, 181, 263, 283, 353, 383, 461, 521, 523, 613, 643, 661, 691, 761, 811, 881, 991, 1013, 1021, 1153, 1181, 1201, 1231, 1483, 1511, 1523, 1531, 1571, 1693, 1783, 1901, 1931, 2083, 2293, 2341, 2351, 2671, 2693, 2741

Offset: 1

James S. DeArmon, Jul 17 2024

nonn

			5 is a term because 5, 5+48, and 5+96 are all prime.

Cf. A001223, A033451, A047948, A052188, A052189, A052190, A279765.

is(n)=isprime(n+96) && isprime(n+48) && isprime(n) \\ Charles R Greathouse IV, Jul 25 2024

a(n) >> n log^3 n. - Charles R Greathouse IV, Jul 25 2024

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A329578 First of three consecutive primes with common gap 48.

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A128312 List of triples of primes with common difference 12.

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A374719 Primes p such that p + 48 and p + 96 are also prime.

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