A052195 Primes p such that p, p+30, p+60 are consecutive primes.

69593, 110651, 134609, 228647, 237791, 250889, 303157, 318919, 396449, 421913, 498271, 507431, 535243, 554317, 629623, 642427, 642457, 668243, 692161, 716003, 729791, 780523, 782581, 790897, 801217, 825131, 829289, 847393, 892291, 902873, 940097, 942449, 963913, 995243, 1027067

Offset: 1

Author

Labos Elemer, Jan 28 2000

Keywords

• nonn

Examples

			69593, 69623, 69653 are consecutive primes with equal distance d = 30.
110651, 110681 and 110711 are consecutive primes with equal distance d = 30.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)
• OEIS wiki, Consecutive primes in arithmetic progression: CPAP with given gap, updated Jan. 2020.

Crossrefs

Subsequence of A124596 (primes followed by gap 30).

Cf. A047948 (analog for gap 6), A052188 (gap 12), A052189 (gap 18), A052190 (gap 24), A053075 (a(n) + 30).

Cf. A001223 (gaps), A052243 (quadruplets with gap 30), A033451 (quadruplets with gap 6).

Programs

Mathematica

Select[Partition[Prime[Range[80000]],3,1],Differences[#]=={30,30}&][[All,1]] (* Harvey P. Dale, May 03 2018 *)

PARI

vecextract(A124596, select(t->t==30, A124596[^1]-A124596[^-1],1)) \\ Terms of A124596 with indices of first differences of 30. Gives a(1..230) from A124596(1..10^4). - M. F. Hasler, Jan 02 2020

Formula

{ A124596(n) | A124596(n+1) = A124596(n) + 30 }. - M. F. Hasler, Jan 02 2020