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

1,1

Links

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

Example

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}

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 *)

Prog

(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

Crossrefs

Cf. A005237, A067889

Sequence in context: A054692 A056256 A329403 * A340573 A043139 A043919

Adjacent sequences: A171664 A171665 A171666 * A171668 A171669 A171670

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 14 2009

Extensions

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

Status

approved