A138254 Balanced prime numbers n such that n*(n-1)-1 is a balanced prime.

10657, 15161, 422911, 691709, 735877, 816239, 1025267, 1030511, 1471891, 1618937, 1683497, 2125411, 2322367, 2448961, 2776157, 2856461, 2880949, 3027319, 3091409, 3114509, 3183337, 3642479, 3797539, 3858091, 3894181, 4752031, 5383387, 5832467, 6052927, 6077821

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Example

10657 is balanced prime, 10657*10656-1=113560991 is balanced prime
(113560973(prev)+113561009(next))/2=113560991

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, 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]

Crossrefs

Cf. A006562.

Sequence in context: A013904 A317417 A317418 * A154510 A157326 A207261

Adjacent sequences: A138251 A138252 A138253 * A138255 A138256 A138257

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 05 2008

Extensions

a(9)-a(30) from Donovan Johnson, Aug 24 2011

Status

approved