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

1,1

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

Mathematica

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

Crossrefs

Cf. A112037.

Sequence in context: A232751 A371795 A155046 * A033318 A093780 A101307

Adjacent sequences: A236385 A236386 A236387 * A236389 A236390 A236391

Keyword

nonn,easy

Author

Joseph L. Pe, Jan 24 2014

Status

approved