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A138264 Balanced prime numbers n such that n*(n-1)+1 is a balanced prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 23:13 EDT 2022. Contains 353847 sequences. (Running on oeis4.)