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A270003 Least prime p such that n = p + q - r for some primes q and r with q > p.

%I A270003 #5 Apr 29 2016 00:12:12
%S A270003 3,2,2,2,2,2,2,2,3,2,2,2,2,2,3,2,2,2,2,2,3,2,2,2,3,2,3,2,2,2,2,2,3,2,
%T A270003 3,2,2,2,3,2,2,2,2,2,3,2,2,2,3,2,3,2,2,2,3,2,3,2,2,2,2,2,3,2,3,2,2,2,
%U A270003 3,2,2,2,2,2,3,2,3,2,2,2,3,2,2,2,3,2
%N A270003 Least prime p such that n = p + q - r for some primes q and r with q > p.
%C A270003 p = 3 when n is an odd nonprime and p = 2 otherwise, so that 3 appears in positions given by A014076.
%H A270003 Clark Kimberling, <a href="/A270003/b270003.txt">Table of n, a(n) for n = 1..10000</a>
%e A270003 n   p   q   r
%e A270003 1   3   5   7
%e A270003 2   2   3   3
%e A270003 3   2   3   2
%e A270003 4   2   5   3
%e A270003 5   2   5   2
%e A270003 6   2   7   3
%e A270003 7   2   7   2
%t A270003 t = Join[{{1, {3, 5, 7}}, {2, {2, 3, 3}}}, Table[If[PrimeQ[n], {n, {2, n, 2}}, p = If[EvenQ[2 + NextPrime[n, 1] - n], 3, 2]; NestWhile[# + 1 &, 1, ! PrimeQ[r = (p + (q = NextPrime[n, #])) - n] &]; {n, {p, q, r}}], {n, 3, 300}]];
%t A270003 Map[#[[2]][[1]] &, t] (* p, A270003 *)
%t A270003 Map[#[[2]][[2]] &, t] (* q, A270753 *)
%t A270003 Map[#[[2]][[3]] &, t] (* r, A271353 *)
%t A270003 (* _Peter J. C. Moses_, Apr 26 2016 *)
%o A270003 (PARI) a(n)=if(n%2 && !isprime(n), 3, 2) \\ _Charles R Greathouse IV_, Apr 29 2016
%Y A270003 Cf. A000040, A270753, A271353.
%K A270003 nonn,easy
%O A270003 1,1
%A A270003 _Clark Kimberling_, Apr 26 2016