A053075 Primes p such that p-30, p, p+30 are consecutive primes.

69623, 110681, 134639, 228677, 237821, 250919, 303187, 318949, 396479, 421943, 498301, 507461, 535273, 554347, 629653, 642457, 642487, 668273, 692191, 716033, 729821, 780553, 782611, 790927, 801247, 825161, 829319, 847423, 892321, 902903

Offset: 1

Author

Harvey P. Dale, Feb 25 2000

Keywords

• easy
• nonn

Comments

Original name: Primes p(k) such that p(k) - p(k-1) = p(k+1) - p(k) = 30.

Examples

			110681 is separated from both the next lower prime and the next higher prime by 30
		

Links

• Zak Seidov, Table of n, a (n) for n = 1 .. 1000

Crossrefs

Cf. A052195 (a(n)-30: first of the triplets) and cross-references there.

Subsequence of A124596 (primes followed by gap 30).

Programs

Mathematica

lst={}; Do[p=Prime[n]; If[p-Prime[n-1] == Prime[n+1]-p == 6*5, AppendTo[lst,p]], {n,2,2*8!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 20 2010 *)

PARI

is_A053075(n)={precprime(n-1)==n-30&&nextprime(n+1)==n+30&&isprime(n)} \\ M. F. Hasler, Jan 02 2020

Formula

a(n) = A052195(n) + 30. - Zak Seidov, Dec 21 2012

A052195 = { A124596(n) | A124596(n-1) = A124596(n) - 30 }. - M. F. Hasler, Jan 02 2020

Extensions

Name edited to conform with style sheet and A052195 etc. - M. F. Hasler, Jan 02 2020