A294639 a(n) = least prime p such that n divides p + prime(n).

2, 3, 7, 5, 19, 5, 11, 5, 13, 11, 2, 11, 11, 13, 13, 11, 43, 11, 47, 29, 11, 31, 101, 7, 3, 3, 5, 5, 7, 7, 59, 29, 61, 31, 61, 29, 139, 103, 67, 67, 67, 29, 67, 71, 73, 31, 71, 17, 67, 71, 73, 73, 607, 19, 73, 17, 73, 19, 313, 19, 83, 17, 71, 73, 337, 13, 71

Offset: 1

Author

Rémy Sigrist, Nov 05 2017

Keywords

• nonn
• look

Comments

This sequence was inspired by A134204.

The logarithmic scatterplot of the sequence has interesting features (see Links section).

We observe runs of consecutive equal terms:

- first pair: a(12) = a(13) = 11,

- first triple: a(39) = a(40) = a(41) = 67,

- first quadruple: a(24980) = a(24981) = a(24982) = a(24983) = 12983.

a(1) = prime(1).

a(2) = prime(2).

Examples

			For n=3:
- prime(3) = 5,
- 3 does not divide 2 + 5,
- 3 does not divide 3 + 5,
- 3 does not divide 5 + 5,
- 3 divides 7 + 5,
- hence a(3) = 7.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Logarithmic scatterplot of the sequence for n=1..50000
• Rémy Sigrist, Colored logarithmic scatterplot of the sequence for n=1..50000 (where the color is function of (a(n) + prime(n))/n)

Crossrefs

Cf. A134204, A254862.

Programs

PARI

a(n) = my (q=prime(n)); forprime(p=2,, if ((p+q)%n==0, return (p)))