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 A304903 Least prime p such that 2*n^2 - p is prime. 3
 3, 5, 3, 3, 5, 19, 19, 5, 3, 3, 5, 7, 3, 7, 3, 7, 5, 3, 3, 5, 31, 7, 23, 13, 31, 5, 19, 13, 11, 43, 19, 17, 3, 3, 13, 7, 31, 5, 13, 3, 11, 7, 19, 23, 3, 61, 5, 3, 7, 5, 61, 37, 5, 3, 3, 7, 19, 3, 7, 31, 7, 5, 13, 3, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Each square > 1 can be written as the average of 2 primes p1 < p2. a(n) gives the least prime p1 such that n^2 = (p1 + p2) / 2. The corresponding p2 is provided in A304904. LINKS Table of n, a(n) for n=2..66. FORMULA a(n) = n^2 - A304905(n) = A304904(n) - 2*A304905(n). EXAMPLE a(5) = 3 because 2*5^2 - 3 = 47 is prime, a(7) = 19 because 2*7^2 - 19 = 71 is prime, whereas all of 98 - 3 = 95, 98 - 5 = 93, 98 - 7 = 91, 98 - 11 = 87, 98 - 13 = 85 and 98 - 17 = 81 are composite. MATHEMATICA f[n_] := Block[{p = 2}, While[ !PrimeQ[2 n^2 - p], p = NextPrime@ p]; p]; Array[f, 65, 2] (* Robert G. Wilson v, May 20 2018 *) PROG (PARI) a(n) = forprime(p=3, , if(ispseudoprime(2*n^2-p), return(p))) \\ Felix Fröhlich, May 20 2018 CROSSREFS Cf. A304874, A304875, A304904, A304905. Sequence in context: A358790 A021287 A124887 * A097524 A073703 A175019 Adjacent sequences: A304900 A304901 A304902 * A304904 A304905 A304906 KEYWORD nonn AUTHOR Hugo Pfoertner, May 20 2018 STATUS approved

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Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)