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.

Showing 1-4 of 4 results.

A275492 Number of primitive weird numbers (A002975) between 10^n and 10^(n+1).

Original entry on oeis.org

0, 1, 1, 5, 6, 11, 24, 37, 67, 124, 223, 382
Offset: 0

Views

Author

M. F. Hasler, Jul 30 2016

Keywords

Comments

It is not known unconditionally whether there are infinitely many primitive weird numbers (PWN, A002975), although numerical data provides strong evidence: even the number of weird numbers of the form 2^k*p*q (A258882, A258333) seems to increase rapidly as k increases. Melfi has shown that Cramer's conjecture implies the infiniteness of PWN.

Links

Crossrefs

Cf. A002975, A006037, A258333, A258882, A275491, A275493, A275494.

Programs

  • PARI
    a(n)=sum(n=10^n\2+1,5*10^n,is_A002975(n*2))

Extensions

Wrong initial term removed and a(11) added by Amiram Eldar, Sep 02 2023

A275493 Number of primitive weird numbers (A002975) below 2^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 6, 8, 9, 10, 14, 16, 20, 24, 29, 33, 46, 55, 61, 79, 87, 103, 128, 152, 173, 234, 266, 313, 403, 483, 561, 756, 850, 940
Offset: 0

Views

Author

M. F. Hasler, Jul 30 2016

Keywords

Comments

It is not known unconditionally whether there are infinitely many primitive weird numbers (PWN, A002975), although numerical data provides strong evidence: even the number of weird numbers of the form 2^k*p*q (A258882, A258333) seems to increase rapidly as k increases. Melfi has shown that Cramer's conjecture implies the infiniteness of PWN.

Links

Crossrefs

Cf. A002975, A006037, A258333, A258882, A275494, A275491, A275492.

Programs

  • PARI
    vector(40,n,#select(t->t<2^n,A002975)) \\ assuming that A002975 is defined as a set, vector or list with enough terms.

Extensions

a(0) inserted, a(39) corrected, and a(40) added by Amiram Eldar, Sep 02 2023

A275494 Number of primitive weird numbers (A002975) between 2^n and 2^(n+1).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 3, 2, 1, 1, 4, 2, 4, 4, 5, 4, 13, 9, 6, 18, 8, 16, 25, 24, 21, 61, 32, 47, 90, 80, 78, 195, 94, 90
Offset: 0

Views

Author

M. F. Hasler, Jul 30 2016

Keywords

Comments

It is not known unconditionally whether there are infinitely many primitive weird numbers (PWN, A002975), although numerical data provides strong evidence: even the number of weird numbers of the form 2^k*p*q (A258882, A258333) seems to increase rapidly as k increases. Melfi has shown that Cramer's conjecture implies the infiniteness of PWN.

Examples

			The first primitive weird numbers are 70, 836, 4030, 5830, 7192, 7912, 9272, 10792, ..., so there is one between 2^6 and 2^7 = 128, one between 2^9 and 2^10 = 1024, one between 2^11 and 2^12 = 4096, three between 2^12 and 2^13, etc.

Links

Crossrefs

Cf. A002975, A006037, A258333, A258882, A275493, A275491, A275492.

Programs

  • PARI
    a(n)=sum(n=2^n\2+1,2^n,is_A002975(n*2))

Formula

a(n) = A275493(n+1) - A275493(n).

Extensions

a(39) from Amiram Eldar, Sep 02 2023

A306951 Number of weird numbers (A006037) below 10^n.

Original entry on oeis.org

0, 1, 2, 7, 204, 1765, 15554, 173709, 1756426, 17270452, 172559761
Offset: 1

Views

Author

Amiram Eldar, Mar 17 2019

Keywords

Comments

Benkoski and Erdős proved that the asymptotic density of weird numbers is positive, thus lim_{n->oo} a(n)/10^n = c > 0. Is c = 0.0017...?

Examples

			The only weird number below 100 is 70 which is larger than 10, thus a(1) = 0 and a(2) = 1.

Links

Crossrefs

Cf. A006037, A275487, A275491, A302992.

Extensions

a(11) from Amiram Eldar, May 26 2023
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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