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.

A062018 a(n) = n^n written backwards.

Original entry on oeis.org

1, 4, 72, 652, 5213, 65664, 345328, 61277761, 984024783, 1, 116076113582, 6528440016198, 352295601578203, 61085552860021111, 573958083098398734, 61615590737044764481, 771467633688162042728, 42457573569257080464393
Offset: 1

Views

Author

Amarnath Murthy, Jun 01 2001

Keywords

Examples

			a(5) = 5213, as 5^5 = 3125.
		

Crossrefs

Programs

  • Maple
    with(numtheory):for n from 1 to 50 do a := convert(n^n,base,10):b := add(10^(nops(a)- i)*a[i],i=1..nops(a)):printf(`%d,`,b); od:
  • Mathematica
    Table[IntegerReverse[n^n],{n,20}] (* Harvey P. Dale, Jul 31 2022 *)
  • PARI
    a(n) = { fromdigits(Vecrev(digits( n^n )))} \\ Harry J. Smith, Jul 29 2009

Formula

a(n) = A004086(n^n).

Extensions

More terms from Jason Earls and Vladeta Jovovic, Jun 01 2001

A302092 Product of n-th Bell number and n-th Bell number written backwards.

Original entry on oeis.org

1, 1, 4, 25, 765, 1300, 61306, 682306, 1713960, 1567246464, 67208788225, 51487177320, 33511259427028, 2030336608089664, 42761083701194302, 7549007599307190895, 776831192562116876947, 3388911887796350381712, 649070202541887765091474, 43774861324581222789850945
Offset: 0

Views

Author

Vincenzo Librandi, Apr 01 2018

Keywords

Comments

Conjecture: in this sequence only two semiprimes (4,25).

Examples

			a(4) = 765 because Bell(4) = 15 and 15*51 = 765.
s(5) = 1300 because Bell(5) = 52 and 52*25 = 1300.
		

Crossrefs

Programs

  • Magma
    [Bell(n)*Seqint(Reverse(Intseq(Bell(n)))): n in [0..30]];
    
  • Maple
    b:= proc(n) option remember; `if`(n=0, 1,
          add(b(n-j)*binomial(n-1, j-1), j=1..n))
        end:
    a:= n-> b(n)*(s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||(b(n))):
    seq(a(n), n=0..25);  # Alois P. Heinz, Apr 26 2018
  • Mathematica
    BellB[#] FromDigits[Reverse[IntegerDigits[BellB[#]]]]&/@Range[0, 50]
    # IntegerReverse[#]&/@BellB[Range[0,20]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 29 2019 *)
  • Perl
    use ntheory ":all"; sub Bell {vecsum(map{stirling($[0],$,2)} 0..$[0])}  for (0..30) { my $b=Bell($); print "$ ",vecprod($b,scalar(reverse($b))),"\n" } # _Dana Jacobsen, Mar 04 2019

Formula

a(n) = A000110(n)*A004098(n).

A322924 Sum of n-th Bell number and n-th Bell number written backwards.

Original entry on oeis.org

2, 2, 4, 10, 66, 77, 505, 1655, 4554, 95259, 695486, 754446, 12166721, 101089109, 414897413, 6841551376, 84604250548, 123761716632, 1633685476445, 13337764677442, 79077443378087, 632521435125225, 7744164113623377, 108500061705109490, 1428467362263664833
Offset: 0

Views

Author

Vincenzo Librandi, Mar 12 2019

Keywords

Comments

After 2, the next prime Bell number is a(110), which has 131 digits.

Examples

			a(4) = 66 because Bell(4) = 15 and 15 + 51 = 66.
a(5) = 77 because Bell(5) = 52 and 52 + 25 = 77.
		

Crossrefs

Programs

  • Magma
    [Bell(n) + Seqint(Reverse(Intseq(Bell(n)))): n in [0..30]];
  • Maple
    g:= proc(n) local L,i;
    L:= convert(n,base,10);
    n + add(L[-i]*10^(i-1),i=1..nops(L))
    end proc:
    map(g @ combinat:-bell, [$0..30]); # Robert Israel, Mar 13 2019
  • Mathematica
    BellB[#] + FromDigits[Reverse[IntegerDigits[BellB[#]]]]&/@Range[0, 30]

Formula

a(n) = A000110(n) + A004098(n).
Showing 1-3 of 3 results.