A079021 -id:A079021 - cp's OEIS frontend

A242476 Primes p such that p + 22 is also prime.

7, 19, 31, 37, 61, 67, 79, 109, 127, 151, 157, 211, 229, 241, 271, 331, 337, 367, 379, 397, 409, 421, 439, 457, 487, 499, 541, 547, 571, 577, 619, 631, 661, 739, 751, 787, 859, 907, 919, 991, 997, 1009, 1039, 1069, 1087, 1129, 1171, 1201, 1237, 1279, 1297

Offset: 1

Vincenzo Librandi, May 21 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A033560, A079021, A153419.

[p: p in PrimesUpTo(1500)| IsPrime(p+22)];

Select[Prime[Range[900]], PrimeQ[# + 22] &]

A079022 Suppose p and q = p + 2*n are primes. Define the difference pattern of (p, q) to be the successive differences of the primes in the range p to q. There are a(n) possible difference patterns.

Original entry on oeis.org

1, 2, 3, 5, 5, 14, 15, 17, 49, 56, 51, 175, 150, 148, 666, 581, 561, 1922, 1449

Offset: 1

Labos Elemer, Jan 24 2003

			n=4, d=8: there are five difference patterns: [8], [6,2], [2,6], [2,4,2], [2,2,4]. The last pattern is singular with prime 4-tuple {p=3,5,7,11=q}.

See A079016, A079017, A079018, A079019, A079020, A079021 for cases n=6 through 11.

Cf. A000230, A079023, A079024.

t[x_] := Table[Length[FactorInteger[x+j]], {j, 0, d}]; p[x_] := Flatten[Position[Table[PrimeQ[x+2*j], {j, 0, d/2}], True]]; dp[x_] := Delete[RotateLeft[p[x]]-p[x], -1]; k=0; d=12; {n1=2, n2=2000, h0=PrimePi[n1], h=PrimePi[n2]}; t1={}; Do[s=Prime[n]; If[PrimeQ[s + d], k=k+1; Print[{k, s, pt=2*dp[s]}]; t1=Union[t1, {2*dp[s]}], 1], {n, h0, h}]; {d, n1, n2, Length[t1], t1} (* program for d=12; partition list is enlargable if t1={} is replaced with already obtained set *)

a(14)-a(17) and a(19) from David A. Corneth, Aug 30 2019

a(18) from Jinyuan Wang, Feb 16 2021

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A242476 Primes p such that p + 22 is also prime.

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