A236388 Primes in order of first appearance among the prime factors of p+1 where p is a prime.

3, 2, 7, 5, 19, 11, 31, 17, 37, 13, 23, 79, 41, 29, 97, 53, 43, 139, 47, 71, 157, 83, 59, 199, 67, 211, 229, 61, 131, 271, 137, 307, 103, 107, 109, 331, 337, 113, 173, 367, 379, 127, 197, 439, 227, 163, 499, 101, 73, 263, 547, 281, 577, 293, 601, 607

Offset: 1

Author

Joseph L. Pe, Jan 24 2014

Keywords

• nonn
• easy

Comments

The first p+1 (p prime) is 2+1=3, so 3 is the first term of the sequence. The next is 3+1=4=2*2, and the prime 2 appears next, so it is the second term of the sequence. The next p+1 = 5+1 = 6 gives no new prime factor; neither do 7+1 = 8 and 11+1 = 12. 13+1 = 14 = 2*7 gives the new prime factor 7, so 7 is the third term of the sequence.

If "p+1" is changed to "p-1" we get A112037. - N. J. A. Sloane, Jan 24 2014

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A112037.

Programs

Mathematica

DeleteDuplicates[ First /@ Flatten[FactorInteger[1 + Prime@Range@200], 1]] (* Giovanni Resta, Jan 24 2014 *)