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 1-3 of 3 results.

A049530 pi(n) associated with A049529.

Original entry on oeis.org

842, 842, 842, 842, 843, 1444, 5169, 15961, 45612, 363035, 363036, 364472, 368073, 403471, 403489, 403489, 403490, 403494, 403585, 404089, 404172, 725931, 730924
Offset: 1

Views

Author

G. L. Honaker, Jr.

Keywords

Examples

			a(5)=843 because pi(6521)=6!+5!+2!+1!=843.

Links

Crossrefs

Cf. A000720, A049529.

Formula

a(n) = A000720(A049529(n)). - Michel Marcus, Aug 14 2020

A066457 Numbers k such that product of factorials of digits of k equals pi(k) (A000720).

Original entry on oeis.org

13, 1512, 1520, 1521, 12016, 12035, 226130351, 209210612202, 209210612212, 209210612220, 209210612221, 13030323000581525
Offset: 1

Views

Author

Jason Earls, Jan 02 2002

Keywords

Comments

The Caldwell/Honaker paper does not discuss this, only suggests further areas of investigation.
There are no other members of the sequence up to and including n=1000000. - Harvey P. Dale, Jan 07 2002
If 10n is in the sequence and 10n+1 is composite then 10n+1 is also in the sequence (the proof is easy). - Farideh Firoozbakht, Oct 24 2008
a(13) > 10^19 if it exists. - Chai Wah Wu, May 03 2018

Examples

			12016 is a term because there are exactly 1!*2!*0!*1!*6! (or 1440) prime numbers less than or equal to 12016.
pi(209210612202) = 8360755200 = 2!*0!*9!*2!*1!*0!*6!*1!*2!*2!*0!*2!. [Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008]

Links

Crossrefs

Cf. A000720, A066459, A049529, A105327.

Programs

  • Mathematica
    Select[Range[1000000], Times@@( # !&/@IntegerDigits[ # ])==PrimePi[ # ]&]
  • PARI
    isok(n) = my(d = digits(n)); prod(k=1, #d, d[k]!) == primepi(n); \\ Michel Marcus, May 04 2018

Extensions

a(7) from Farideh Firoozbakht, Apr 20 2005
a(8)-a(11) from Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008
a(12) from Chai Wah Wu, May 03 2018

A101702 Numbers m such that the sum of the factorials of their digits is equal to the reversal of m.

Original entry on oeis.org

1, 2, 541, 52100, 58504, 66410, 430000, 863180, 8601400, 17927300, 27927300, 31000000, 665100000, 3715000000, 6739630000, 11000000000, 21000000000, 53100000000, 70858000000, 79637300000, 451000000000, 1715000000000, 2715000000000, 48304000000000, 340000000000000, 5520000000000000
Offset: 1

Views

Author

Farideh Firoozbakht, Dec 24 2004

Keywords

Comments

If s=sum of the factorials of digits of m & reversal(m) >= s then 10^(reversal(m) - s)*m is in the sequence. Example m=23; s = 2! + 3!; reversal(23) - s = 24 & 23*10^24 is in the sequence. So this sequence is infinite because there exist infinitely many numbers m such that reversal(m) > s. If m is a k-digit term of this sequence and the first digit of m is 1 then 10^(k-1) + m is also in the sequence. Examples: m=1 so 10^(1-1) + 1 = 2 is in the sequence, m=17927300 so 10^7 + 17927300 = 27927300 is in the sequence. If m > 5 then 10 divides a(m). If 10 doesn't divide a(m) then the reversal of m is in the sequence A014080, so all terms of A014080 are: reversal(1), reversal(2), reversal(541) & reversal(58504).

Examples

			665100000 is in the sequence because reversal(665100000) = 1566 = 6! + 6! + 5! + 1! + 0! + 0! + 0! + 0! + 0!.

Crossrefs

Cf. A014080, A049529, A101697.

Programs

  • Mathematica
    Do[h = IntegerDigits[n]; l = Length[h]; If[FromDigits[Reverse[IntegerDigits[n]]] == Sum[h[[k]]!, {k, l}], Print[n]], {n, 10^9}]

Extensions

More terms from Donovan Johnson, Feb 26 2008
Showing 1-3 of 3 results.

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

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