A085434 Twice odd isolated primes.

46, 74, 94, 106, 134, 158, 166, 178, 194, 226, 254, 262, 314, 326, 334, 346, 422, 446, 466, 502, 514, 526, 554, 586, 614, 634, 662, 674, 706, 718, 734, 746, 758, 766, 778, 794, 802, 818, 878, 886, 898, 914, 934, 958, 974, 982, 998, 1006, 1018, 1082, 1094

Offset: 6

Author

Cino Hilliard, Aug 13 2003

Keywords

• easy
• nonn

Comments

Name was: n-th even number not a power of 2 whose largest and smallest factors do not add or subtract to a twin prime. - Robert Israel, Mar 11 2025

The density of these numbers approach 0 as n approaches oo.

Crossrefs

Cf. A052369, A056608, A134797.

Programs

Maple

P:= select(isprime, {seq(i,i=3..1000,2)}):
A:= P minus (P +~ 2) minus (P -~ 2):
sort(convert(A,list)) *~ 2; # Robert Israel, Mar 11 2025

PARI

maxpmmintwin(n) = { c=0; forprime(p=3,n, if(!isprime(p-2) & !isprime(p+2),print1(p+p","); c++); ); print(); print(c" "c/n+.0) }

Formula

a(n) = 2 * A134797(n).

Extensions

Definition corrected by Robert Israel, Mar 11 2025