A138264 Balanced prime numbers n such that n*(n-1)+1 is a balanced prime.

150571, 998353, 1719517, 3942889, 4476187, 5290699, 5651869, 6041701, 6089521, 6553117, 8018089, 9046627, 9606349, 10990489, 11460859, 11466769, 12573283, 12997483, 13082617, 13152817, 13334701, 14774971, 16240597, 16319179, 17335501, 17445397, 18814261

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 05 2008

Keywords

• nonn

Crossrefs

Cf. A006562.

Programs

Mathematica

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*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]
bpnQ[{a_,b_,c_}]:=Module[{d=b(b-1)+1,e,f},e=NextPrime[d,-1];f= NextPrime[ d]; (a+c)/2==b&&PrimeQ[d]&&(e+f)/2==d]; Select[Partition[Prime[ Range[ 1200000]],3,1],bpnQ][[All,2]] (* Harvey P. Dale, May 12 2017 *)

Extensions

a(11)-a(27) from Donovan Johnson, Aug 24 2011