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A126938
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a(1) = 3, a(n) = the smallest prime p > a(n-1) such that (a(n-1)+p)/2 is prime.
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5
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3, 7, 19, 43, 79, 127, 151, 163, 199, 223, 331, 367, 379, 439, 487, 607, 619, 643, 739, 883, 991, 1051, 1087, 1171, 1231, 1327, 1471, 1627, 1699, 1747, 1759, 1987, 1999, 2179, 2383, 2551, 2683, 2731, 2767, 3067, 3259, 3343, 3571, 3643, 3739, 3847, 3907
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OFFSET
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1,1
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COMMENTS
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Starting with a(2)=7 all terms are 7 mod 12. - Zak Seidov, Feb 26 2017
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LINKS
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EXAMPLE
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(3+7)/2=5 prime, (7+19)/2=13 prime, (19+43)/2=31 prime, etc.
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MAPLE
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A[1]:= 3: A[2]:= 7:
for n from 3 to 100 do A[n]:= f(A[n-1]) od:
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MATHEMATICA
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s={3}; pn=3; n=PrimePi[pn]; Do[Do[p=Prime[i]; If[PrimeQ[(pn+p)/2], AppendTo[s, p]; pn=p; n=i; Break[]], {i, n+1, 10000}], {112}]; s
sp[n_]:=Module[{p=NextPrime[n]}, While[!PrimeQ[(n+p)/2], p=NextPrime[p]]; p]; NestList[sp, 3, 50] (* Harvey P. Dale, Apr 12 2013 *)
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PROG
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(PARI) step(q)=forprime(p=q+1, , if(isprime((p+q)/2), return(p)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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