editing

approved

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

(PARI) a(n)=if(n%2 && !isprime(n), 3, 2) \\ Charles R Greathouse IV, Apr 29 2016

proposed

editing

editing

proposed

allocated Least prime such that n = p + q - r for Clark Kimberlingsome prime q > p and some prime r.

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

1,1

p = 3 when n is an odd nonprime and p = 2 otherwise, so that 3 appears in positions given by A014076.

Clark Kimberling, <a href="/A270003/b270003.txt">Table of n, a(n) for n = 1..10000</a>

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

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 *)

Cf. A000040, A270753, A271353.

allocated

nonn,easy

Clark Kimberling, Apr 26 2016

approved

editing

allocated for Clark Kimberling

allocated

approved