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 A159828 a(n) is smallest number m > 0 such that m^2 + n^2 + 1 is prime. 3
 1, 6, 1, 6, 9, 2, 3, 6, 1, 6, 3, 2, 3, 6, 1, 6, 27, 8, 9, 24, 1, 6, 21, 4, 69, 12, 3, 6, 21, 6, 3, 6, 1, 6, 9, 2, 9, 6, 1, 6, 15, 6, 9, 6, 1, 6, 27, 2, 3, 36, 9, 6, 3, 6, 15, 18, 1, 48, 3, 4, 9, 6, 7, 6, 15, 4, 21, 42, 5, 6, 3, 2, 69, 18, 5, 6, 3, 2, 9, 24, 1, 6, 3, 8, 9, 6, 11, 18, 15, 4, 3, 6, 7, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(2k-1) is odd, a(2k) is even. There are infinitely many primes of the forms n^2 + m^2 and n^2 + m^2 + 1, but it is not known if the number of primes of the form n^2 + 1 is infinite; cf. comments in A002496, A002313, A079544. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE n = 1: 1^2 + 1^2 + 1 = 3 is prime, so a(1) = 1. n = 2: 1^2 + 2^2 + 1 = 6, 2^2 + 2^2 + 1 = 9, 3^2 + 2^2 + 1 = 14, 4^2 + 2^2 + 1 = 21, 5^2 + 2^2 + 1 = 30 are composite, but 6^2 + 2^2 + 1 = 41 is prime, so a(2) = 6. n = 27: 1^2 + 27^2 + 1 = 731 = 17*43, 2^2 + 27^2 + 1 = 734 = 2*367 are composite, but 3^2 + 27^2 + 1 = 739 is prime, so a(27) = 3. MATHEMATICA snm[n_]:=Module[{c=n^2+1, x=NextPrime[n^2+1]}, While[!IntegerQ[Sqrt[x-c]], x= NextPrime[x]]; Sqrt[x-c]]; Array[snm, 100] (* Harvey P. Dale, Sep 22 2018 *) PROG (MAGMA) S:=[]; for n in [1..100] do q:=n^2+1; m:=1; while not IsPrime(m^2+q) do m+:=1; end while; Append(~S, m); end for; S; // Klaus Brockhaus, May 21 2009 CROSSREFS Cf. A069003 (smallest d such that n^2+d^2 is prime), A002496 (primes of form n^2+1), A002313 (primes of form x^2+y^2), A079544 (primes of form x^2+y^2+1, x>0, y>0). Sequence in context: A222068 A272055 A157292 * A131114 A199230 A199101 Adjacent sequences:  A159825 A159826 A159827 * A159829 A159830 A159831 KEYWORD easy,nonn AUTHOR Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 23 2009 EXTENSIONS Edited and extended by Klaus Brockhaus, May 21 2009 STATUS approved

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Last modified April 23 07:37 EDT 2021. Contains 343201 sequences. (Running on oeis4.)