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 A260870 Least k>0 such that k^2 + (2n+1-k)^2 is prime, or 0 if no such k exists. 2
 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 5, 4, 2, 1, 2, 1, 3, 4, 2, 2, 5, 4, 1, 1, 2, 3, 5, 3, 1, 2, 6, 3, 1, 5, 4, 5, 4, 1, 2, 2, 1, 4, 1, 2, 2, 3, 3, 2, 5, 7, 1, 3, 3, 1, 2, 1, 4, 1, 1, 4, 1, 4, 1, 2, 2, 5, 3, 3, 1, 2, 1, 5, 4, 1, 5, 1, 3, 2, 10, 2, 1, 3, 6, 1, 2, 1, 4, 1, 5, 10, 3, 3, 2, 10, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS It appears that any odd number N = 2n+1 > 1 (and also N = 2, hence all primes, see A260869) can be written as the sum of two positive integers such that the sum of their squares is prime. For an even number > 2 this is obviously not possible since k and 2n-k have the same parity and therefore the sum of their squares is even. The record values 1, 2, 3, 5, 6, 7, 10, 13, 16, 29, 30, 37, 40, 41, 49, 55, 64, 67, 68, 74, 85, 88, 106, 128, ... occur for indices n (half of the odd numbers 2n+1) 1, 4, 6, 15, 35, 54, 83, 121, 172, 281, 936, 1093, 1150, 1240, 3121, 4126, 5116, 6793, 11935, 12556, 18238, 32710, 33343, 57256, ... LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 MATHEMATICA lk[n_]:=Module[{k=1}, While[!PrimeQ[k^2+(2n+1-k)^2], k++]; k]; Array[lk, 100] (* Harvey P. Dale, May 31 2017 *) PROG (PARI) A260870(n)=for(k=1, (n=2*n+1)\2, isprime(k^2+(n-k)^2)&&return(k)) CROSSREFS Sequence in context: A226006 A210943 A260869 * A282497 A087157 A138618 Adjacent sequences:  A260867 A260868 A260869 * A260871 A260872 A260873 KEYWORD nonn AUTHOR M. F. Hasler, Aug 09 2015 STATUS approved

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Last modified April 6 11:38 EDT 2020. Contains 333273 sequences. (Running on oeis4.)