A025621 -id:A025621 - cp's OEIS frontend

A108779 Numbers of the form (10^i)*(11^j), with i, j >= 0.

1, 10, 11, 100, 110, 121, 1000, 1100, 1210, 1331, 10000, 11000, 12100, 13310, 14641, 100000, 110000, 121000, 133100, 146410, 161051, 1000000, 1100000, 1210000, 1331000, 1464100, 1610510, 1771561, 10000000, 11000000, 12100000, 13310000

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 26 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A025612, A025616, A025621, A025625, A025629, A025632, A025634, A025635, A108761, A003596, A003597, A107988, A003598, A108698, A003599, A107788, A108687, A108090.

import Data.Set (singleton, deleteFindMin, insert)
a108779 n = a108779_list !! (n-1)
a108779_list = f $ singleton (1,0,0) where
   f s = y : f (insert (10 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
         where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015

n = 10^7; Flatten[Table[10^i*11^j, {i, 0, Log10[n]}, {j, 0, Log[11, n/10^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Sum_{n>=1} 1/a(n) = (10*11)/((10-1)*(11-1)) = 11/9. - Amiram Eldar, Sep 25 2020

a(n) ~ exp(sqrt(2*log(10)*log(11)*n)) / sqrt(110). - Vaclav Kotesovec, Sep 25 2020

A107462 Numbers of the form (4^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 4, 13, 16, 52, 64, 169, 208, 256, 676, 832, 1024, 2197, 2704, 3328, 4096, 8788, 10816, 13312, 16384, 28561, 35152, 43264, 53248, 65536, 114244, 140608, 173056, 212992, 262144, 371293, 456976, 562432, 692224, 851968, 1048576, 1485172

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 09 2005

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A107326.

Cf. A025617, A025618, A025619, A025620, A025621, A107364, A107466, A108056, A108090.

n = 10^6; Flatten[Table[4^i*13^j, {i, 0, Log[4, n]}, {j, 0, Log[13, n/4^i]}]] // Sort (* Amiram Eldar, Sep 24 2020 *)

Sum_{n>=1} 1/a(n) = (4*13)/((4-1)*(13-1)) = 13/9. - Amiram Eldar, Sep 24 2020

a(n) ~ exp(sqrt(2*log(4)*log(13)*n)) / sqrt(52). - Vaclav Kotesovec, Sep 24 2020

A025686 Exponent of 10 (value of j) in n-th number of form 4^i*10^j.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 2, 1, 0, 2, 1, 3, 0, 2, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 5, 2, 4, 1, 3, 0, 5, 2, 4, 1, 6, 3, 0, 5, 2, 4, 1, 6, 3, 0, 5, 2, 7, 4, 1, 6, 3, 0, 5, 2, 7, 4, 1, 6, 3, 0, 8, 5, 2, 7, 4, 1, 6, 3, 0, 8, 5, 2, 7, 4, 1, 9, 6, 3, 0, 8, 5, 2, 7, 4, 1, 9, 6, 3, 0, 8, 5, 2, 10, 7, 4, 1, 9, 6, 3, 0, 8, 5, 2, 10

Offset: 1

David W. Wilson

nonn

Cf. A025621. Differs from A025657 at a(114). A025649 is the exponent of 4.

A025649 Exponent of 4 (value of i) in n-th number of form 4^i*10^j.

Original entry on oeis.org

0, 1, 0, 2, 1, 3, 0, 2, 4, 1, 3, 0, 5, 2, 4, 1, 6, 3, 0, 5, 2, 7, 4, 1, 6, 3, 8, 0, 5, 2, 7, 4, 9, 1, 6, 3, 8, 0, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 13, 0, 5, 10, 2, 7, 12, 4, 9, 14, 1, 6, 11, 3, 8, 13, 0, 5, 10, 15, 2, 7, 12, 4, 9, 14, 1, 6, 11, 16, 3, 8, 13, 0, 5, 10

Offset: 1

David W. Wilson

nonn

Cf. A025621. Differs from A025641 at a(114). A025686 is exponent of 10.

A025742 a(n) is the index of 10^n within sequence of numbers of form 4^i*10^j.

Original entry on oeis.org

1, 3, 7, 12, 19, 28, 38, 50, 64, 79, 96, 115, 135, 157, 181, 206, 233, 262, 292, 324, 358, 393, 430, 469, 509, 551, 595, 640, 687, 736, 786, 838, 892, 947, 1004, 1063, 1123, 1185, 1249, 1314, 1381, 1450, 1520, 1592, 1666, 1741, 1818, 1897, 1977, 2059, 2143, 2228

Offset: 0

David W. Wilson

Indices m for which A025649(m) is 0. - Michel Marcus, Jan 10 2018

			The index of 10^0 in A025621 is 1, so a(0)=1.
The index of 10^1 in A025621 is 3, so a(1)=3.
The index of 10^2 in A025621 is 7, so a(2)=7.

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Cf. A025621, A025649, A025686.

a(n)=my(N=1); n+1+sum(i=1,n, logint(N*=10,4)); \\ Charles R Greathouse IV, Jan 10 2018

first(n)=my(s,N=1/10); vector(n+1,i, s+=logint(N*=10,4)+1) \\ Charles R Greathouse IV, Jan 10 2018

Offset changed by Michel Marcus, Jan 10 2018

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A108779 Numbers of the form (10^i)*(11^j), with i, j >= 0.

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A107462 Numbers of the form (4^i)*(13^j), with i, j >= 0.

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A025686 Exponent of 10 (value of j) in n-th number of form 4^i*10^j.

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A025649 Exponent of 4 (value of i) in n-th number of form 4^i*10^j.

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A025742 a(n) is the index of 10^n within sequence of numbers of form 4^i*10^j.

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