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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A141704 Indices of records in A141703.

Original entry on oeis.org

1, 2, 3, 4, 11, 14, 47, 193, 331, 2967, 5557
Offset: 1

Views

Author

M. F. Hasler, Jul 01 2008

Keywords

Comments

Based on an idea by Jack Brennen, who pointed out that 2221=prime(331) yields the value A141703(331)=29.
No more terms below 50000. The corresponding records are 0, 1, 3, 6, 7, 11, 17, 22, 29, 32, 40, ... - Amiram Eldar, Sep 25 2019

Examples

			The sequence starts 1,2,3,4,... since the first 4 terms in A141703 are not preceded by a value larger or equal to them.
a(5) = 11 since A141703(11)=6 is the next record value.
a(9) = 331 since A141703(331)=29 is the 9th value establishing a (quite long-lasting) record.

Crossrefs

Cf. A002997 and references therein; A087788; A141702 ff.

Programs

  • PARI
    m=-1;for(n=1,10^4, m < A141703(n) & print1(n," /*",m=A141703(n),"*/, "));

Extensions

a(10)-a(11) from Amiram Eldar, Sep 25 2019

A141702 a(n) is the number of Carmichael numbers of the form prime(n)*prime(n')*prime(n") with n > n' > n".

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 3, 1, 2, 0, 0, 0, 0, 1
Offset: 1

Views

Author

M. F. Hasler, Jun 30 2008

Keywords

Comments

The formula and PARI code uses Korselt's criterion. This sequence is a somewhat trivial variant of the more interesting sequence giving the number of Carmichael numbers of the form prime(n)*prime(n')*prime(n") with n < n' < n" (known to be finite for given n).

Examples

			a(7)=2 is the first nonzero term since 561 = 3*11*17 and 1105 = 5*13*17 are the two smallest Carmichael numbers and there's no other Carmichael number having prime(7)=17 as largest factor.

Links

Crossrefs

Cf. A002997 and references therein ; A087788 ; A141703 ff.

Programs

  • PARI
    A141702(n) = { local( p=prime(n), c=0 ); forprime( q=5,p-2, forprime( r=3,q-2, (p*q*r-1)%(p-1)==0 && (p*q*r-1)%(q-1)==0 && (p*q*r-1)%(r-1)==0 && c++ ));c }

Formula

a(n) = # { pqr | p=prime(n) > q=prime(n') > r=prime(n") ; p-1 | pqr-1 ; q-1 | pqr-1 ; r-1 | pqr-1 }
Showing 1-2 of 2 results.

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