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

1,1

Links

Table of n, a(n) for n=1..27.

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 *)

Crossrefs

Cf. A006562.

Sequence in context: A051651 A065324 A262195 * A343679 A246285 A344940

Adjacent sequences: A138261 A138262 A138263 * A138265 A138266 A138267

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 05 2008

Extensions

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

Status

approved