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.

A107988 Numbers of the form (4^i)*(11^j), with i, j >= 0.

Original entry on oeis.org

1, 4, 11, 16, 44, 64, 121, 176, 256, 484, 704, 1024, 1331, 1936, 2816, 4096, 5324, 7744, 11264, 14641, 16384, 21296, 30976, 45056, 58564, 65536, 85184, 123904, 161051, 180224, 234256, 262144, 340736, 495616, 644204, 720896, 937024, 1048576
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jun 12 2005

Keywords

Links

Crossrefs

Subsequence of A003596.
Cf. A025617, A025618, A025619, A025620, A025621, A107462, A003597, A003598, A003599, A108090.

Programs

  • Haskell
    import Data.Set (singleton, deleteFindMin, insert)
a107988 n = a107988_list !! (n-1)
a107988_list = f $ singleton (1,0,0) where
   f s = y : f (insert (4 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
         where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015
  • Mathematica
    n = 10^6; Flatten[Table[4^i*11^j, {i, 0, Log[4, n]}, {j, 0, Log[11, n/4^i]}]] // Sort (* Amiram Eldar, Sep 24 2020 *)

Formula

Sum_{n>=1} 1/a(n) = (4*11)/((4-1)*(11-1)) = 22/15. - Amiram Eldar, Sep 24 2020
a(n) ~ exp(sqrt(2*log(4)*log(11)*n)) / sqrt(44). - Vaclav Kotesovec, Sep 24 2020

A108761 Numbers of the form (10^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 10, 13, 100, 130, 169, 1000, 1300, 1690, 2197, 10000, 13000, 16900, 21970, 28561, 100000, 130000, 169000, 219700, 285610, 371293, 1000000, 1300000, 1690000, 2197000, 2856100, 3712930, 4826809, 10000000, 13000000, 16900000
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jun 24 2005

Keywords

Links

Crossrefs

Cf. A107326, A107364, A107462, A107466, A107710, A108056, A107764, A108748, A108090.

Programs

  • Haskell
    import Data.Set (singleton, deleteFindMin, insert)
a108761 n = a108761_list !! (n-1)
a108761_list = f $ singleton (1,0,0) where
   f s = y : f (insert (10 * y, i + 1, j) $ insert (13 * y, i, j + 1) s')
         where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015
  • Mathematica
    n = 10^7; Flatten[Table[10^i*13^j, {i, 0, Log10[n]}, {j, 0, Log[13, n/10^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Formula

Sum_{n>=1} 1/a(n) = (10*13)/((10-1)*(13-1)) = 65/54. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(10)*log(13)*n)) / sqrt(130). - Vaclav Kotesovec, Sep 25 2020

A107710 Numbers of the form (6^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 6, 13, 36, 78, 169, 216, 468, 1014, 1296, 2197, 2808, 6084, 7776, 13182, 16848, 28561, 36504, 46656, 79092, 101088, 171366, 219024, 279936, 371293, 474552, 606528, 1028196, 1314144, 1679616, 2227758, 2847312, 3639168, 4826809, 6169176
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jun 10 2005

Keywords

Links

Crossrefs

Cf. A025626, A025627, A025628, A025629, A064476, A107326, A107364, A107462, A107466, A108056, A108090.

Programs

  • Mathematica
    n = 10^6; Flatten[Table[6^i*13^j, {i, 0, Log[6, n]}, {j, 0, Log[13, n/6^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Formula

Sum_{n>=1} 1/a(n) = (6*13)/((6-1)*(13-1)) = 13/10. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(6)*log(13)*n)) / sqrt(78). - Vaclav Kotesovec, Sep 25 2020

A107764 Numbers of the form (8^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 8, 13, 64, 104, 169, 512, 832, 1352, 2197, 4096, 6656, 10816, 17576, 28561, 32768, 53248, 86528, 140608, 228488, 262144, 371293, 425984, 692224, 1124864, 1827904, 2097152, 2970344, 3407872, 4826809, 5537792, 8998912, 14623232, 16777216
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jun 11 2005

Keywords

Links

Crossrefs

Cf. A025633, A025634, A107326, A107364, A107462, A107466, A107710, A108056, A108090.

Programs

  • Mathematica
    n = 10^6; Flatten[Table[8^i*13^j, {i, 0, Log[8, n]}, {j, 0, Log[13, n/8^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Formula

Sum_{n>=1} 1/a(n) = (8*13)/((8-1)*(13-1)) = 26/21. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(8)*log(13)*n)) / sqrt(104). - Vaclav Kotesovec, Sep 25 2020

A108748 Numbers of the form (9^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 9, 13, 81, 117, 169, 729, 1053, 1521, 2197, 6561, 9477, 13689, 19773, 28561, 59049, 85293, 123201, 177957, 257049, 371293, 531441, 767637, 1108809, 1601613, 2313441, 3341637, 4782969, 4826809, 6908733, 9979281, 14414517, 20820969
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jun 23 2005

Keywords

Links

Crossrefs

Cf. A025635, A108687, A107326, A107364, A107462, A107466, A107710, A108056, A107764, A108090.

Programs

  • Mathematica
    n = 10^6; Flatten[Table[9^i*13^j, {i, 0, Log[9, n]}, {j, 0, Log[13, n/9^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Formula

Sum_{n>=1} 1/a(n) = (9*13)/((9-1)*(13-1)) = 39/32. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(9)*log(13)*n)) / sqrt(117). - Vaclav Kotesovec, Sep 25 2020

A108771 Numbers of the form (12^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 12, 13, 144, 156, 169, 1728, 1872, 2028, 2197, 20736, 22464, 24336, 26364, 28561, 248832, 269568, 292032, 316368, 342732, 371293, 2985984, 3234816, 3504384, 3796416, 4112784, 4455516, 4826809, 35831808, 38817792, 42052608, 45556992
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jun 25 2005

Keywords

Links

Crossrefs

Cf. A107326, A107364, A107462, A107466, A107710, A108056, A107764, A108748, A108761, A108090.

Programs

  • Maple
    N:= 10^8: # to get all terms <= N
sort([seq(seq(12^i*13^j, j = 0 .. floor(log[13](N/12^i))), i=0..floor(log[12](N)))]); # Robert Israel, Jun 16 2019
  • Mathematica
    With[{max = 5*10^7}, Flatten[Table[12^i*13^j, {i, 0, Log[12, max]}, {j, 0, Log[13, max/12^i]}]] // Sort] (* Amiram Eldar, Mar 29 2025 *)

Formula

Sum_{n>=1} 1/a(n) = 13/11. - Amiram Eldar, Mar 29 2025
Showing 1-6 of 6 results.

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