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A237057
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a(n) = smallest prime > a(n-1) such that a(n)+4n is also prime.
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1
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2, 3, 5, 7, 13, 17, 19, 31, 41, 43, 61, 83, 89, 97, 101, 103, 109, 113, 127, 151, 191, 193, 223, 239, 241, 283, 293, 311, 331, 347, 359, 367, 419, 431, 433, 461, 463, 499, 509, 521, 523, 563, 571, 601, 647, 659, 673, 719, 727, 733, 797, 809, 811, 821, 823, 829
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OFFSET
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0,1
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COMMENTS
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Many twin primes belong to the sequence, for example (41, 43) and (191, 193).
Many consecutive primes also appear such as (13, 17) and (83, 89).
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LINKS
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EXAMPLE
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a(5)=17 since 17+4*5=17+20=37 is prime. 11+4*4=27 is not prime, so 11 is not in the sequence.
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MATHEMATICA
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nxt[{n_, p_}]:=Module[{np=NextPrime[p]}, While[!PrimeQ[np+4(n+1)], np = NextPrime[ np]]; {n+1, np}]; Transpose[NestList[nxt, {0, 2}, 60]][[2]] (* Harvey P. Dale, Feb 26 2015 *)
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PROG
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(PARI) a237057(maxp) = {my(a=[2], n=1); forprime(p=3, maxp, if(isprime(p+4*n), n++; a=concat(a, p))); a} \\ Colin Barker, Feb 12 2014
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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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