A178382 Primes that are in classes k+ and k- for some k in the Erdős-Selfridge classification of primes.

2, 3, 5, 7, 17, 29, 41, 43, 61, 79, 101, 131, 137, 149, 173, 197, 211, 223, 227, 229, 233, 239, 241, 251, 271, 281, 293, 307, 311, 331, 353, 397, 439, 449, 463, 523, 569, 593, 607, 641, 683, 691, 727, 733, 751, 761, 787, 821, 853, 859, 919, 947, 953, 983, 1031

Offset: 1

Author

T. D. Noe, May 26 2010

Keywords

• nonn

Comments

The first five terms are the only primes in both class 1+ and class 1-. The Mathematica program assigns 2 and 3 to class 0 in order to simplify the algorithm; they are actually in classes 1- and 1+.

Programs

Mathematica

classp[2]=0; classp[3]=0; SetAttributes[classp, Listable]; classp[p_] := classp[p] = 1+Max@@classp[First/@FactorInteger[p+1]]; classm[2]=0; classm[3]=0; SetAttributes[classm, Listable]; classm[p_] := classm[p] = 1+Max@@classm[First/@FactorInteger[p-1]]; Select[Prime[Range[1000]], classp[ # ]==classm[ # ]&]

Formula

Prime(n) such that A126433(n) = A126805(n).