cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A247834 Maximal non-semiprime number which is a "preprime" of the n-th kind (defined in comment in A247395).

Original entry on oeis.org

8, 45, 125, 343, 325, 833, 1331, 1573, 2197, 2057, 3211, 3289, 4913, 4901, 6859, 6647, 8303, 10051, 10469, 11191, 12167, 15341, 16399, 17081, 18259, 22103, 24389, 26071, 29791, 27347, 31117, 35557, 36163, 36859, 39401, 42439, 50653, 50933, 52111, 56129, 56699
Offset: 1

Views

Author

Vladimir Shevelev, Sep 24 2014

Keywords

Comments

Conjecture: the sequence contains all cubes of primes, except for 3^3 (cf. A030078).
Prime(n)^3 is in the sequence iff the interval [prime(n)^(3/2), prime(n)*sqrt(prime(n+1))] contains a prime.
A simple algorithm for finding the position k=k(n) for which a(k) = prime(n)^3 is given in A247835 (see formula and example there).
Conjecture: every term has the form a(n)= p*q*r, where p<=q<=r are primes.

Links

Crossrefs

Cf. A030078, A156759, A247393, A247394, A247395, A247396, A247509, A247510, A247511, A247606, A247835, A247867.

Extensions

More terms from Peter J. C. Moses, Sep 24 2014

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

Original entry on oeis.org

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

Views

Author

Vladimir Shevelev, Sep 24 2014

Keywords

Comments

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

Examples

			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.

Crossrefs

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

Programs

  • 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

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).

Extensions

More terms from Jinyuan Wang, Feb 17 2021

A288882 Primes of the form k!3 + 3^6, where k!3 is the triple factorial number (A007661).

Original entry on oeis.org

733, 739, 757, 809, 1009, 1609, 13049, 210169, 81359229952729, 126757680265216729, 13106744139423334400729, 2295148179742698933452800729, 12931890526958090978845347074978621685760000729
Offset: 1

Views

Author

Robert Price, Jun 18 2017

Keywords

Links

Crossrefs

Cf. A007661, A247467, A247867.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 3] + 3^6, {i, 0, 100}], PrimeQ[#]&]

Formula

a(n) = 729 + A007661(A247467(n)). - Elmo R. Oliveira, Apr 20 2025
Showing 1-3 of 3 results.

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