A247835 Indices of prime(n)^3 in A247834, or a(n)=0 if prime(n)^3 is not in A247834.

1, 0, 3, 4, 7, 9, 13, 15, 21, 27, 29, 37, 43, 47, 52, 61, 71, 74, 83, 89, 94, 105, 111, 123, 138, 145, 149, 158, 161, 168, 196, 208, 220, 226, 246, 248, 261, 276, 287, 299, 316, 319, 340, 345, 358, 364, 392, 422, 432, 436, 447, 464, 470, 496, 512, 530, 544, 549

Offset

1,3

Comments

Conjecture: all a(n)>0, except for n=2.

Links

Table of n, a(n) for n=1..58.

Formula

If prime(n)^3 is in A247834, then a(n) = pi(prime(n)^(3/2)) - n + 1, where pi(x) is the prime counting function (A000720).

Example

Using the formula, let us find the position in A247834, in which should be 17^3, if 17^3 belongs to A247834. Since 17 = prime(7), then we have a(7) = pi(17^(3/2)) - 6 = pi(70) - 6 = 13. Indeed, A247834(13) = 4913 = 17^3.

Prog

(PARI) a(n) = my(p=prime(n)); if(nextprime(ceil(p*sqrt(p))) > p*sqrt(prime(n+1)), 0, primepi(prime(n)^(3/2)) - n + 1); \\ Jinyuan Wang, Feb 17 2021

Crossrefs

Cf. A030078, A156759, A247393, A247394, A247395, A247396, A247509, A247510, A247511, A247606, A247834, A247867.

Sequence in context: A203623 A053099 A073273 * A072441 A152032 A004652

Adjacent sequences: A247832 A247833 A247834 * A247836 A247837 A247838

Keyword

nonn

Author

Vladimir Shevelev, Sep 24 2014

Extensions

More terms from Jinyuan Wang, Feb 17 2021

Status

approved