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.

Previous Showing 11-13 of 13 results.

A260229 a(n) = floor(e^(n!)).

Original entry on oeis.org

2, 7, 403, 26489122129, 13041808783936322797338790280986488113446079415755132
Offset: 1

Views

Author

Ilya Gutkovskiy, Jul 20 2015

Keywords

Comments

The exponential growth in the number of permutations of n elements.
Next term is too big to be included.

Examples

			a(1) = floor(e^(1!)) = floor(e) = 2.
		

Crossrefs

Programs

  • Mathematica
    Table[Floor[E^n!], {n, 1, 7}]
  • PARI
    default(realprecision, 100); vector(5, n, floor(exp(n!))) \\ Michel Marcus, Aug 06 2015

Formula

a(n) = A000149(A000142(n)).
a(n) = floor(sqrt(e^A052849(n) - e^A000142(n) + sqrt(e^A052849(n) - e^A000142(n) + sqrt(e^A052849(n) - e^A000142(n) + ...)))).

A261071 a(n) = 2^(n!) + 1.

Original entry on oeis.org

3, 5, 65, 16777217, 1329227995784915872903807060280344577
Offset: 1

Views

Author

Marco RipĂ , Aug 08 2015

Keywords

Comments

a(n) is a sum of two k-th powers of positive integers for k=1,2,...,n.

Examples

			a(3) = 2^6 + 1 = 65.
		

Crossrefs

Cf. A050923.

Programs

Formula

a(n) = 2^(n!) + 1.
a(n) = A050923(n) + 1.

A291042 One powerful arithmetic progression with nontrivial difference and maximal length.

Original entry on oeis.org

10529630094750052867957659797284314695762718513641400204044879414141178131103515625, 94766670852750475811618938175558832261864466622772601836403914727270603179931640625, 179003711610750898755280216553833349827966214731903803468762950040400028228759765625, 263240752368751321698941494932107867394067962841035005101121985353529453277587890625, 347477793126751744642602773310382384960169710950166206733481020666658878326416015625
Offset: 1

Views

Author

Martin Renner, Aug 16 2017

Keywords

Comments

This sequence has the maximal length of a powerful arithmetic progression for which the k-th term is a k-th power.
The originating sequence is 1, 9, 17, 25, 33 with difference 8. This sequence is multiplied by 3^24*5^30*11^24*17^20 to generate a(n) with common difference 84237040758000422943661278378274517566101748109131201632359035313129425048828125000.
Note that this sequence is just an example of a maximal progression. Similar progressions with smaller terms are provided by 2^15*3^24*5^40*13^24 * {11, 18, 25, 32, 39}, 37^24 * {213, 169, 125, 81, 37}, or, if negative terms are allowed, by 2^15*5^20 * {11, 8, 5, 2, -1}. - Giovanni Resta, Aug 29 2017

Examples

			a(1) is obviously a first power.
a(2) = 307841957589849138828884412917083740234375^2 is a square.
a(3) = 5635779747116948576103515625^3 is a third power.
a(4) = 716288998461106640625^4 is a fourth power.
a(5) = 51072299355515625^5 is a fifth power.
		

Crossrefs

Cf. A050923.
Previous Showing 11-13 of 13 results.