A176180 -id:A176180 - cp's OEIS frontend

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

Vladimir Joseph Stephan Orlovsky, Apr 11 2010

nonn

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

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

Cf. A063091, A176180.

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 *)

Definition clarified by Jonathan Sondow, Feb 03 2012

A176182 Primes p(n) such that gcd(p(n)-1, p(n+1)-1) < gcd(p(n)+1, p(n+1)+1).

Original entry on oeis.org

7, 19, 23, 43, 47, 53, 67, 79, 83, 103, 127, 131, 139, 163, 167, 173, 223, 233, 251, 257, 263, 293, 307, 353, 359, 379, 383, 409, 439, 443, 463, 467, 479, 487, 491, 499, 503, 509, 557, 563, 587, 593, 643, 647, 653, 677, 683, 709, 719, 739, 743, 797, 823, 829

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 11 2010

nonn

Cf. A063091, A176180, A176181.

lst={};Do[p0=Prime[n];p1=Prime[n+1];If[GCD[p0-1,p1-1]Harvey P. Dale, Jul 06 2011 *)

cp's OEIS Frontend

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

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