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 A109197 Minimal value of k > 0 such that n^2 + k^2 is semiprime. 10
 2, 3, 9, 1, 3, 1, 7, 3, 1, 1, 11, 1, 1, 3, 3, 1, 3, 3, 11, 1, 9, 2, 1, 2, 11, 1, 3, 4, 1, 1, 1, 2, 7, 5, 1, 1, 7, 4, 5, 1, 7, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 5, 2, 5, 4, 1, 1, 1, 1, 1, 2, 1, 1, 5, 7, 3, 1, 9, 1, 11, 4, 3, 2, 1, 2, 1, 1, 1, 14, 5, 2, 5, 1, 1, 5, 1, 6, 7, 2, 1, 2, 7, 1, 1, 6, 13, 8, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Table of n, a(n) for n=0..100. FORMULA a(n) = minimal value of k > 0 such that n^2 + k^2 is semiprime. EXAMPLE a(0) = 2 because 0^2 + 1^2 = 1 is not semiprime, but 0^2 + 2^2 = 4 = 2^2 is. a(1) = 3 because 1^2 + 1^2 and 1^2 + 2^2 are not semiprime, but 1^2 + 3^2 = 10 = 2 * 5 is semiprime. a(81) = 14 because 81^2 + 14^2 = 6757 = 29 * 233 and for no smaller k>0 is 81^2 + k^2 a semiprime. a(100) = 1 because 100^2 + 1^2 = 10001 = 73 * 137. MATHEMATICA k2sp[n_]:=Module[{k=1}, While[PrimeOmega[n^2+k^2]!=2, k++]; k]; Array[ k2sp, 110, 0] (* Harvey P. Dale, Oct 30 2016 *) PROG (PARI) A109197(n)={local(r); r=1; while(bigomega(n^2+r^2)<>2, r=r+1); r} \\ Michael B. Porter, May 13 2010 CROSSREFS Cf. A001358, A108714. Sequence in context: A011163 A155983 A201407 * A021811 A280987 A030367 Adjacent sequences: A109194 A109195 A109196 * A109198 A109199 A109200 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Jun 21 2005 STATUS approved

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Last modified August 14 16:37 EDT 2024. Contains 375166 sequences. (Running on oeis4.)