A171667 Lesser of a pair of twin primes (p,p+2) sandwiched between two numbers (p-1,p+3) having the same number of divisors.

11, 29, 59, 431, 599, 827, 1031, 1319, 1619, 1787, 2111, 2141, 2267, 2687, 2711, 3299, 3329, 3371, 3527, 3671, 4001, 4091, 4229, 4259, 5021, 5099, 5519, 5867, 6299, 6659, 6779, 7331, 7457, 8087, 8231, 8387, 8627, 8861, 8999, 9419, 9461, 9767, 10139

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 14 2009

Keywords

• nonn

Examples

			First term 11: 10={1,2,5,10},14={1,2,7,14} Second term 29: 28={1,2,4,7,14,28},32={1,2,4,8,16,32}
		

Links

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

Crossrefs

Cf. A005237, A067889

Programs

Mathematica

f[n_]:=Length[Divisors[n]]; lst={};Do[p=Prime[n];If[PrimeQ[p+2]&&f[p-1]==f[p+3],AppendTo[lst,p]],{n,7!}];lst
Select[Range[11000],DivisorSigma[0,#-1]==DivisorSigma[0,#+3]&&AllTrue[{#, #+2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 04 2019 *)

PARI

forprime(p=o=0,1e4,(2+o==o=p)&&numdiv(p-3)==numdiv(p+1)&&print1(p-2",")) \\ M. F. Hasler, Jul 31 2015

Extensions

Name edited by M. F. Hasler, Jul 31 2015