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

1,1

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.

Links

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

Formula

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

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

Example

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

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

Prog

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

Crossrefs

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

Sequence in context: A354791 A107976 A022557 * A297261 A296705 A297138

Adjacent sequences: A307543 A307544 A307545 * A307547 A307548 A307549

Keyword

nonn

Author

Peter Dolland, Apr 14 2019

Status

approved