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 A059843 a(n) is the smallest prime p such that p-n is a square. 4
 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 Moshe Levin, Table of n, a(n) for n = 1..10000 FORMULA Min{p| p-n=x^2 for some x; x>0, p is prime}. EXAMPLE n=17: {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53}-17= {-15,...,-4,0,2,6,12,14,20,24,26,30,36}. The first square difference is obtained with 53, the smallest such prime. The square arising here is usually 1. MAPLE for n from 1 to 200 do k := 0: c := true: while(c) do k := k+1: if(isprime(k^2+n)) then c := false: end if: end do: a[n] := k^2+n: end do: seq(a[j], j=1..200); CROSSREFS These terms arise in A002496, A056899, A049423, A005473, A056905, A056909 as first or 2nd entries depending on offset. A002496, A056899, A049423, A005473, A056905, A056909. Sequence in context: A085399 A063696 A069587 * A092927 A071553 A021812 Adjacent sequences:  A059840 A059841 A059842 * A059844 A059845 A059846 KEYWORD nonn AUTHOR Labos E. (labos(AT)ana.sote.hu), Feb 26 2001 STATUS approved

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