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 A059843 a(n) is the smallest prime p such that p-n is a nonzero square. 3
 2, 3, 7, 5, 41, 7, 11, 17, 13, 11, 47, 13, 17, 23, 19, 17, 53, 19, 23, 29, 37, 23, 59, 73, 29, 107, 31, 29, 173, 31, 47, 41, 37, 43, 71, 37, 41, 47, 43, 41, 617, 43, 47, 53, 61, 47, 83, 73, 53, 59, 67, 53, 89, 79, 59, 137, 61, 59, 383, 61, 97, 71, 67, 73, 101, 67, 71, 149, 73 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Zak Seidov, Table of n, a(n) for n = 1..10000 FORMULA a(n) = min{p : p - n = x^2 for some x > 0, p is prime}. Does a(n) exist for all n? - Jianing Song, Feb 04 2019 EXAMPLE For n = 17, let P = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,...} be the set of primes, then P - 17 = {-15,...,-4,0,2,6,12,14,20,24,26,30,36,...}. The first positive square in P - 17 is 36 with p = 53, so a(17) = 53. The square arising here is usually 1. MAPLE SearchLimit := 100; for n from 1 to 400 do k := 0: c := true: while(c and k < SearchLimit) do k := k + 1: c := not isprime(k^2+n): end do: if k = SearchLimit then error("Search limit reached!") fi; a[n] := k^2 + n end do: seq(a[j], j=1..400); # Edited and SearchLimit introduced by Peter Luschny, Feb 05 2019 MATHEMATICA spsq[n_]:=Module[{p=NextPrime[n]}, While[!IntegerQ[Sqrt[p-n]], p= NextPrime[ p]]; p]; Array[spsq, 70] (* Harvey P. Dale, Nov 10 2017 *) PROG (PARI) for(n=1, 100, for(k=1, 100, if(isprime(k^2+n), print1(k^2+n, ", "); break()))) \\ Jianing Song, Feb 04 2019 (PARI) a(n) = forprime(p=n, , if ((p-n) && issquare(p-n), return (p))); \\ Michel Marcus, Feb 05 2019 CROSSREFS These terms arise in A002496, A056899, A049423, A005473, A056905, A056909 as first or 2nd entries depending on offset. Cf. A002496, A056899, A049423, A005473, A056905, A056909. Cf. A056896 (where p-n can be 0). Sequence in context: A332211 A353075 A069587 * A092927 A071553 A021812 Adjacent sequences: A059840 A059841 A059842 * A059844 A059845 A059846 KEYWORD nonn AUTHOR Labos Elemer, Feb 26 2001 STATUS approved

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Last modified July 23 08:15 EDT 2024. Contains 374546 sequences. (Running on oeis4.)