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A270003
Least prime p such that n = p + q - r for some primes q and r with q > p.
5
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, 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, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2
OFFSET
1,1
COMMENTS
p = 3 when n is an odd nonprime and p = 2 otherwise, so that 3 appears in positions given by A014076.
LINKS
EXAMPLE
n p q r
1 3 5 7
2 2 3 3
3 2 3 2
4 2 5 3
5 2 5 2
6 2 7 3
7 2 7 2
MATHEMATICA
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}]];
Map[#[[2]][[1]] &, t] (* p, A270003 *)
Map[#[[2]][[2]] &, t] (* q, A270753 *)
Map[#[[2]][[3]] &, t] (* r, A271353 *)
(* Peter J. C. Moses, Apr 26 2016 *)
PROG
(PARI) a(n)=if(n%2 && !isprime(n), 3, 2) \\ Charles R Greathouse IV, Apr 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 26 2016
STATUS
approved