A176181 Primes p(n) such that gcd(p(n)-1, p(n+1)-1) > gcd(p(n)+1, p(n+1)+1).

13, 31, 37, 61, 73, 89, 97, 109, 113, 151, 157, 181, 193, 199, 211, 229, 241, 271, 277, 313, 331, 349, 367, 373, 389, 397, 401, 421, 433, 449, 457, 523, 541, 571, 601, 607, 613, 619, 631, 661, 673, 691, 701, 727, 733, 751, 757, 761, 769, 811, 853, 877, 929

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 11 2010

Keywords

• nonn

Comments

Sequence does not contain any lesser of twin primes A001359. (Proof. If p(n+1) = p(n)+2, then gcd(p(n)-1, p(n+1)-1) = 2 = gcd(p(n)+1, p(n+1)+1), so p(n) is not a term.) - Jonathan Sondow, Feb 03 2012

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A063091, A176180.

Programs

Mathematica

lst={}; Do[p0=Prime[n]; p1=Prime[n+1]; If[GCD[p0-1,p1-1] > GCD[p0+1,p1+1], AppendTo[lst,p0]], {n,200}]; lst
Transpose[Select[Partition[Prime[Range[200]],2,1],GCD@@(#-1)>GCD@@(#+1)&]] [[1]] (* Harvey P. Dale, Sep 30 2014 *)

Extensions

Definition clarified by Jonathan Sondow, Feb 03 2012