A270003 - OEIS

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A270003

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

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

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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

Clark Kimberling, Table of n, a(n) for n = 1..10000

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

Cf. A000040, A270753, A271353.

Sequence in context: A248743 A085398 A252503 * A067438 A178250 A174550

Adjacent sequences: A270000 A270001 A270002 * A270004 A270005 A270006

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 26 2016

STATUS

approved