login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291042 One powerful arithmetic progression with nontrivial difference and maximal length. 0
10529630094750052867957659797284314695762718513641400204044879414141178131103515625, 94766670852750475811618938175558832261864466622772601836403914727270603179931640625, 179003711610750898755280216553833349827966214731903803468762950040400028228759765625, 263240752368751321698941494932107867394067962841035005101121985353529453277587890625, 347477793126751744642602773310382384960169710950166206733481020666658878326416015625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..5.

John P. Robertson, The maximal length of a powerful arithmetic progression, American Mathematical Monthly 107 (2000), 951.

EXAMPLE

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.

Sequence in context: A095552 A095554 A095556 * A095558 A095560 A095562

Adjacent sequences:  A291039 A291040 A291041 * A291043 A291044 A291045

KEYWORD

nonn,fini,full

AUTHOR

Martin Renner, Aug 16 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 08:33 EDT 2021. Contains 348074 sequences. (Running on oeis4.)