A138254 - OEIS

%I #7 Mar 31 2012 12:38:14

%S 10657,15161,422911,691709,735877,816239,1025267,1030511,1471891,

%T 1618937,1683497,2125411,2322367,2448961,2776157,2856461,2880949,

%U 3027319,3091409,3114509,3183337,3642479,3797539,3858091,3894181,4752031,5383387,5832467,6052927,6077821

%N Balanced prime numbers n such that n*(n-1)-1 is a balanced prime.

%e 10657 is balanced prime, 10657*10656-1=113560991 is balanced prime

%e (113560973(prev)+113561009(next))/2=113560991

%t NextPrime[n_Int]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k];PrevPrime[n_Int]:=Module[{k},k=n-1;While[ !PrimeQ[k],k-- ];k];s="";For[i=2,i< 10^5,p=Prime[i];If[(Prime[i-1]+Prime[i+1])/2==p,r=p*(p-1)-1;a=PrevPrime[r];b=NextPrime[r];If[PrimeQ[r]&&r==(a+b)/2,(*Print[p, ":", a, ",", b, ";", r]*)s=s<>ToString[p]<>","]];i++ ];Print[s]

%Y Cf. A006562.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 05 2008

%E a(9)-a(30) from _Donovan Johnson_, Aug 24 2011