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 A237057 a(n) = smallest prime > a(n-1) such that a(n)+4n is also prime. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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). LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 EXAMPLE 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. MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A108184. Sequence in context: A038903 A136003 A215799 * A183073 A123856 A336721 Adjacent sequences:  A237054 A237055 A237056 * A237058 A237059 A237060 KEYWORD nonn AUTHOR Carmine Suriano, Feb 03 2014 STATUS approved

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Last modified January 19 21:55 EST 2022. Contains 350466 sequences. (Running on oeis4.)