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 1-4 of 4 results.

A085307 a(1) = 1; for n > 1, concatenate distinct prime factors of n in decreasing order.

Original entry on oeis.org

1, 2, 3, 2, 5, 32, 7, 2, 3, 52, 11, 32, 13, 72, 53, 2, 17, 32, 19, 52, 73, 112, 23, 32, 5, 132, 3, 72, 29, 532, 31, 2, 113, 172, 75, 32, 37, 192, 133, 52, 41, 732, 43, 112, 53, 232, 47, 32, 7, 52, 173, 132, 53, 32, 115, 72, 193, 292, 59, 532, 61, 312, 73, 2, 135, 1132, 67
Offset: 1

Views

Author

Labos Elemer, Jun 27 2003

Keywords

Comments

n and a(n) have the same parity.

Examples

			m = 100 = 2*2*5*5 -> {2,5} -> {5,2} -> 52 = a(100);
a(510510) = 1713117532, while A084317(510510) = 2357111317.

Links

Crossrefs

In A084317 the order of factors is increasing.
Cf. A084317, A084318, A084319, A085308, A085309, A084796, A084797.

Programs

  • Maple
    with(numtheory):
a:= n-> parse(cat(`if`(n=1, 1, sort([factorset(n)[]], `>`)[]))):
seq(a(n), n=1..100);  # Alois P. Heinz, May 02 2016
  • Mathematica
    f[n_] := FromDigits[ Flatten[ IntegerDigits /@ Reverse[ Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]]]]; Table[ f[n], {n, 1, 70}]
Table[FromDigits[Flatten[IntegerDigits/@Reverse[FactorInteger[n][[All, 1]]]]],{n,90}] (* Harvey P. Dale, Oct 10 2017 *)

Formula

Algorithm:
1. factorize n;
2. order prime factors by decreasing size;
3. concatenate prime factors and interpret the result as a decimal number.

Extensions

Edited by Robert G. Wilson v, Jul 15 2003

A073646 Least number formed by concatenating the prime factors of n in base 10.

Original entry on oeis.org

1, 2, 3, 22, 5, 23, 7, 222, 33, 25, 11, 223, 13, 27, 35, 2222, 17, 233, 19, 225, 37, 112, 23, 2223, 55, 132, 333, 227, 29, 235, 31, 22222, 113, 172, 57, 2233, 37, 192, 133, 2225, 41, 237, 43, 1122, 335, 223, 47, 22223, 77, 255, 173, 1322, 53, 2333, 115, 2227
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 29 2002

Keywords

Comments

a(n)<=A037276(n) for all n and a(n)=A037276(n) for n<22, a(22) = a(2*11) = 112 <> A037276(22) = 211.

Examples

			a(6) = a(2*3) = 23 < 32; a(66) = a(2*3*11) = 1123 < 1132 < 2113 < 2311 < 3112 < 3211.

Links

Crossrefs

Different from A037276. Cf. A084797.

Programs

  • Haskell
    import Data.List (sort)
a073646 :: Integer -> Integer
a073646 = read . concat . sort . map show . a027746_row
-- Reinhard Zumkeller, Jul 13 2013
  • Mathematica
    con[n_, k_] := Nest[Join[{#}, {n}] &, n, k - 1]; Table[Min[FromDigits /@ Flatten /@ IntegerDigits[Permutations[Flatten[con @@@ FactorInteger[n]]]]], {n, 56}] (* Jayanta Basu, Jul 04 2013 *)

Formula

Sort {A027746(n,k): k=1..A001222(n)} lexicographically and concatenate. - Reinhard Zumkeller, Jul 13 2013

A084796 Replace n with concatenation of its prime factors in decreasing order.

Original entry on oeis.org

1, 2, 3, 22, 5, 32, 7, 222, 33, 52, 11, 322, 13, 72, 53, 2222, 17, 332, 19, 522, 73, 112, 23, 3222, 55, 132, 333, 722, 29, 532, 31, 22222, 113, 172, 75, 3322, 37, 192, 133, 5222, 41, 732, 43, 1122, 533, 232, 47, 32222, 77, 552, 173, 1322, 53, 3332, 115, 7222, 193, 292
Offset: 1

Views

Author

N. J. A. Sloane, Jul 19 2003

Keywords

Links

Crossrefs

Cf. A032726, A085307, A084797.

Programs

  • Maple
    with(numtheory):
a:= n-> parse(cat(`if`(n=1, 1,
    sort([seq(i[1]$i[2], i=ifactors(n)[2])], `>`)[]))):
seq(a(n), n=1..100);  # Alois P. Heinz, May 02 2016
  • Mathematica
    Table[FromDigits[Flatten[Table[#[[1]],#[[2]]]&/@ Reverse[ FactorInteger[ n]]]],{n,60}] (* Harvey P. Dale, Aug 29 2016 *)

Extensions

More terms from Christopher N. Swanson (cswanson(AT)ashland.edu), Jul 22 2003

A106557 Largest number that can be obtained by concatenating the two factors of the n-th semiprime.

Original entry on oeis.org

22, 32, 33, 52, 72, 53, 73, 211, 55, 213, 311, 217, 75, 219, 313, 232, 77, 317, 511, 319, 292, 312, 513, 323, 372, 711, 412, 517, 432, 329, 713, 331, 472, 519, 532, 373, 523, 592, 717, 1111, 612, 413, 433, 719, 672, 473, 712, 1311, 529, 732, 531, 792, 533
Offset: 1

Views

Author

Eric Angelini, May 09 2005

Keywords

Examples

			First semiprime is 4; 4 is 2*2 -> 22.
Second semiprime is 6; 6 is 3*2 -> 32 (and not 23).
...
Eighth semiprime is 22; 22 is 2*11 -> 211 (and not 112).

Links

Crossrefs

Cf. A001358, A084797, A106556.

Programs

  • PARI
    \\ here cd(x,y) returns base 10 concatenation.
cd(v1, v2)={10^(logint(v2,10) + 1)*v1 + v2}
seq(n)={my(v=vector(n), k=0); for(i=1, #v, k++; while(2<>bigomega(k), k++); my(f=factor(k)[,1]); v[i] = if(#f==1, cd(f[1], f[1]), max(cd(f[1], f[2]), cd(f[2], f[1])))); v} \\ Andrew Howroyd, Jan 08 2020

Formula

a(n) = A084797(A001358(n)). - Andrew Howroyd, Jan 08 2020

Extensions

Edited by N. J. A. Sloane, Apr 14 2008
Terms a(22) and beyond from Andrew Howroyd, Jan 08 2020
Showing 1-4 of 4 results.

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

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