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Prime indices of A195685.
1

%I #18 Nov 30 2022 10:28:34

%S 7,14,15,20,26,28,29,36,45,48,66,70,89,98,104,115,122,126,142,152,157,

%T 161,164,167,177,182,186,191,194,199,202,205,216,218,219,244,264,279,

%U 283,295,297,299,324,329,336,342,362,408,416,423,430,440,457,498,500

%N Prime indices of A195685.

%C 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.

%H Alois P. Heinz, <a href="/A307546/b307546.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%e A000040(a(1)) = 17 = A195685(1).

%e A000040(a(5)) = A000040(26) = 101 = A195685(5).

%p with(numtheory):

%p q:= n-> (p-> tau(2*p-1)=4 and tau(2*p+1)=4)(ithprime(n)):

%p select(q, [$1..500])[]; # _Alois P. Heinz_, Apr 18 2019

%o (PARI) isok(k) = my(p=prime(k)); (numdiv(2*p-1) == 4) && (numdiv(2*p+1) == 4); \\ _Michel Marcus_, Nov 30 2022

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

%K nonn

%O 1,1

%A _Peter Dolland_, Apr 14 2019