S000329


Primes having numbers with 2 and 4 prime factors (counting multiplicity) before or after them.

23, 37, 59, 61, 83, 157, 227, 277, 347, 563, 733, 877, 997, 1213, 1237, 1283, 1307, 1523, 2797, 3253, 3517, 3733, 3803, 4547, 5387, 5483, 6037, 6827, 7187, 7213, 7933, 9013, 9133, 9277, 10357, 10883, 12107, 12157, 12227, 12757, 13043, 13093, 13163, 14243

1

S000329

This sequence is the union of the previous two sequences.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

MathOverflow, Are there infinitely many primes p such that both p-1 and p+1 have at most 3 prime factors, counted with multiplicity?

(Mma) Select[Prime[Range[2, 1000000]], (Plus @@ Transpose[FactorInteger[# - 1]][[2]] == 4 && Plus @@ Transpose[FactorInteger[# + 1]][[2]] == 2) || (Plus @@ Transpose[FactorInteger[# - 1]][[2]] == 2 && Plus @@ Transpose[FactorInteger[# + 1]][[2]] == 4) &, 100]

Cf. A079153, A106639, S000327-S000330.

nonn

T. D. Noe, Nov 12 2014

© Tony D Noe 2014-2015