A190821 Prime numbers p where d(p-1) = d(p+1) increases to a record.

7, 19, 41, 199, 919, 5741, 18089, 41651, 90271, 446081, 1276001, 27033161, 43220449, 53308529, 109245401, 512669249, 663929729, 2266639649, 2560742911, 2969200961, 8505402751, 32540473601, 61573368401, 74335064959, 109494811999

Offset: 1

Author

Juri-Stepan Gerasimov, May 21 2011

Keywords

• nonn

Comments

a(26) <= 354208192001. - Donovan Johnson, Jun 03 2011

Examples

			a(1) = 7 because 7 is prime and d(6) = 4 = d(8).
		

Crossrefs

Cf. A145337, A190646 (numbers n such that d(n-1)=d(n+1) increases to a record).

Programs

Mathematica

s = Select[Prime@ Range@ 1000000, DivisorSigma[0, # - 1] == DivisorSigma[0, # + 1] &]; t = DivisorSigma[0, # - 1] & /@ s; a = {0}; b = {0}; Do[If[t[[k]] > Max@ b, AppendTo[a, s[[k]]]]; AppendTo[b, t[[k]]], {k, Length@ s}]; a (* Michael De Vlieger, Oct 30 2015 *)

PARI

r=0; forprime(p=2,4e9,t=numdiv(p-1);if(t>r&t==numdiv(p+1),r=t; print1(p", "))) \\ Charles R Greathouse IV, May 27 2011

Extensions

a(14)-a(21) from Charles R Greathouse IV, May 27 2011

a(22) from Charles R Greathouse IV, May 31 2011

a(23)-a(25) from Donovan Johnson, Jun 03 2011