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 1-6 of 6 results.

A097653 Numbers n such that n=d_1!!+d_2!!+...+d_k!! where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

1, 2, 3, 107
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 10 2004

Keywords

Examples

			107 is in the sequence because 1!!+0!!+7!!=1+1+7*5*3*1=107.

Crossrefs

Cf. A097654, A097655, A097643.

Programs

  • Mathematica
    Do[h=IntegerDigits[n];l=Length[h];If[n==Sum[h[[k]]!!, {k, l}], Print[n]], {n, 4*9!!}]

A097654 Numbers n such that n=|d_1!!-d_2!!+...+(-1)^(k-1)*d_k!!| where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

1, 2, 3, 380
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 10 2004

Keywords

Examples

			380 is in the sequence because 380=|3!!-8!!+0!!|.

Crossrefs

Cf. A097653, A097655, A097643.

Programs

  • Mathematica
    Do[h=IntegerDigits[n];l=Length[h];If[n==Abs[Sum[(-1)^(k-1) *h[[k]]!!, {k, l}]], Print[n]], {n, 4*9!!}]

A110071 Numbers n such that n = pi(d_1!!*d_2!!*...*d_k!!) where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

0, 4, 290, 11387, 1656281, 538311474096
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 22 2005

Keywords

Comments

No other terms below 10^14. - Max Alekseyev, Jul 21 2024

Examples

			11387 is in the sequence because 11387 = pi(1!!*1!!*3!!*8!!*7!!).

Crossrefs

Cf. A000720, A006882, A097655, A110070, A110072.

Programs

  • Mathematica
    Do[h = IntegerDigits[n]; l = Length[h]; If[n == PrimePi[ Product[h[[k]]!!, {k, l}]], Print[n]], {n, 0, 50000}]

Extensions

a(5) added by Farideh Firoozbakht, Dec 02 2007
a(6) from Max Alekseyev, Jul 21 2024

A110072 Numbers k such that k = sigma(d_1!!*d_2!!*...*d_j!!) where d_1 d_2 ... d_j is the decimal expansion of k.

Original entry on oeis.org

1, 163800, 1547520, 81254720
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 22 2005

Keywords

Comments

No more terms up to 10^25. It is very probable that there is no greater term. - Robert Gerbicz, May 09 2008
No other terms below 10^45. - Max Alekseyev, Feb 19 2024

Examples

			81254720 is a term because 81254720 = sigma(8!!*1!!*2!!*5!!*4!!*7!!*2!!*0!!).

Crossrefs

Cf. A000203, A097655, A110070, A110071.

Programs

  • Mathematica
    Do[h = IntegerDigits[n]; l = Length[h]; If[n == DivisorSigma[1, Product[h[[k]]!!, {k, l}]], Print[n]], {n, 0, 100000000}]

A102279 Numbers n such that n = phi(d_1)!*phi(d_2)!* ... *phi(d_k)! where d_1 d_2 ... d_k is the decimal expansion of n and assume that phi(0)=0.

Original entry on oeis.org

1, 48, 720, 17280, 17915904000, 479219999055934390272000000000
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 08 2005

Keywords

Comments

All terms are of the form 2^i*3^j*5^t.
No more terms < 10^100. - David Wasserman, Apr 03 2008

Examples

			17280 is in the sequence because 17280 = phi(1)!*phi(7)!*phi(2)!*phi(8)!*phi(0)!.

Crossrefs

Cf. A097655, A102280, A102281.

A158988 Numbers n such that n=phi(d_1!!)*phi(d_2!!)*...*phi(d_k!!) where d_1...d_k is the decimal expansion of n.

Original entry on oeis.org

4, 16, 64, 128, 6912, 24576, 16384, 786432, 524288, 50096498540544, 3764488749034090683017723904, 167633515663893895281332936606596215078912
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 01 2009, Jul 08 2009

Keywords

Comments

All terms are of the form 2^i*3^j where i and j are nonnegative integers.
So corresponding to each term a(n) of the sequence there exists a unique pair
(i(n),j(n)) such that a(n)=2^i(n)*3^j(n). {n,(i(n),j(n))} for n=1, 2, ...,
24 are: {1,(2,0)},{2,(4,0)},{3,(6,0)},{4,(7,0)},{5,(8,3)},{6,(14,0)},{7,(13,1)},
{8,(19,0)},{9,(18,1)},{10,(36,6)},{11,(71,13)},{12,(110,17)},{13,(206,24)},
{14,(200,30)},{15,(679,118)},{16,(679,123)},{17,(766,136)},{18,(868,158)},
{19,(1032,160)},{20,(1207,199)},{21,(1258,171)},{22,(1257,209)},{23,(1326,199)},
& {24,(3291,531)}. So for example a(10)=2^36*3^6=50096498540544 and a(24), the largest known term of the sequence, is 2^3291*3^531.

Crossrefs

Cf. A097655.
Showing 1-6 of 6 results.

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