A307546 Prime indices of A195685.

7, 14, 15, 20, 26, 28, 29, 36, 45, 48, 66, 70, 89, 98, 104, 115, 122, 126, 142, 152, 157, 161, 164, 167, 177, 182, 186, 191, 194, 199, 202, 205, 216, 218, 219, 244, 264, 279, 283, 295, 297, 299, 324, 329, 336, 342, 362, 408, 416, 423, 430, 440, 457, 498, 500

Offset: 1

Author

Peter Dolland, Apr 14 2019

Keywords

• nonn

Comments

Since only the indices are listed, this sequence is more compact than A195685. As described there, all elements of the triples (2*prime(a(n))-1, 2*prime(a(n)), 2*prime(a(n))+1) are products of exactly two distinct primes. Such values are called "squarefree semiprimes" in A006881.

Examples

			A000040(a(1)) = 17 = A195685(1).
A000040(a(5)) = A000040(26) = 101 = A195685(5).
		

Links

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

Crossrefs

Cf. A000005, A000040, A000720, A006881, A195685.

Programs

Maple

with(numtheory):
q:= n-> (p-> tau(2*p-1)=4 and tau(2*p+1)=4)(ithprime(n)):
select(q, [$1..500])[];  # Alois P. Heinz, Apr 18 2019

PARI

isok(k) = my(p=prime(k)); (numdiv(2*p-1) == 4) && (numdiv(2*p+1) == 4); \\ Michel Marcus, Nov 30 2022

Formula

a(n) = A000720(A195685(n)).

A195685(n) = A000040(a(n)).