A025648 -id:A025648 - cp's OEIS frontend

A025619 Numbers of form 4^i*7^j, with i, j >= 0.

1, 4, 7, 16, 28, 49, 64, 112, 196, 256, 343, 448, 784, 1024, 1372, 1792, 2401, 3136, 4096, 5488, 7168, 9604, 12544, 16384, 16807, 21952, 28672, 38416, 50176, 65536, 67228, 87808, 114688, 117649, 153664, 200704, 262144, 268912, 351232, 458752, 470596

Offset: 1

David W. Wilson

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

Subsequence of A003591.

n=10^6; Flatten[Table[4^i*7^j, {i, 0, Log[4, n]}, {j, 0, Log[7, n/4^i]}]]//Sort (* Amiram Eldar, Sep 24 2020 *)

Sum_{n>=1} 1/a(n) = (4*7)/((4-1)*(7-1)) = 14/9. - Amiram Eldar, Sep 24 2020
a(n) ~ exp(sqrt(2*log(4)*log(7)*n)) / sqrt(28). - Vaclav Kotesovec, Sep 24 2020
a(n) = 4^A025648(n) * 7^A025666(n). - R. J. Mathar, Jul 06 2025

A131579 Period 10: repeat 0, 3, 6, 9, 2, 5, 8, 1, 4, 7.

Original entry on oeis.org

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

Offset: 0

Paul Curtz, Oct 02 2007

a(n) = last digit of 3*n, n >= 0. a(n+7) = last digit of 3*n + 1, n >= 0, and a(n+4) = last digit of 3*n + 2, n >= 0. The last digit of -3*n = A144468(n), n >= 0, the last one of -3*n + 1 = A144468(n+3), n >= 0 and the last one of -3*n + 2 = A144468(n+6), n >= 0. - Wolfdieter Lang, Aug 14 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1)

Cf. A022336, A025648, A025655, A059626, A144468.

&cat[[0,3,6,9,2,5,8,1,4,7]^^10]; // Vincenzo Librandi, Aug 15 2017

PadRight[{}, 120, {0, 3, 6, 9, 2, 5, 8, 1, 4, 7}] (* Vincenzo Librandi, Aug 15 2017 *)

a(n) = A008585(n) mod 10. - Bruno Berselli, Mar 08 2011
G.f.: -x*(3 + 6*x + 9*x^2 + 2*x^3 + 5*x^4 + 8*x^5 + x^6 + 4*x^7 + 7*x^8) / ( (x-1) *(1+x) *(x^4 + x^3 + x^2 + x + 1) *(x^4 - x^3 + x^2 - x + 1) ). - R. J. Mathar, Mar 10 2011
Decimal expansion of 41028683/1111111110 . - R. J. Mathar, Jul 06 2025

A025666 Exponent of 7 (value of j) in n-th number of form 4^i*7^j.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 3, 1, 2, 0, 3, 1, 4, 2, 0, 3, 1, 4, 2, 0, 5, 3, 1, 4, 2, 0, 5, 3, 1, 6, 4, 2, 0, 5, 3, 1, 6, 4, 2, 7, 0, 5, 3, 1, 6, 4, 2, 7, 0, 5, 3, 8, 1, 6, 4, 2, 7, 0, 5, 3, 8, 1, 6, 4, 9, 2, 7, 0, 5, 3, 8, 1, 6, 4, 9, 2, 7, 0, 5, 10, 3, 8, 1, 6, 4, 9, 2, 7, 0, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 0, 5

Offset: 1

David W. Wilson

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A025619, A025648.

N:= 10^10: # to consider all terms with 4^i*7^j<=N
S:= {seq(seq(4^i*7^j, j=0..floor(log[7](N/4^i))),i=0..floor(log[4](N)))}:
map(padic:-ordp, sort(convert(S,list)),7); # Robert Israel, Aug 11 2019

4^A025648(n)*7^a(n) = A025619(n). - Robert Israel, Aug 11 2019

A025722 Index of 7^n within sequence of numbers of form 4^i*7^j.

Original entry on oeis.org

1, 3, 6, 11, 17, 25, 34, 44, 56, 69, 84, 100, 117, 136, 156, 178, 201, 225, 251, 278, 307, 337, 368, 401, 435, 471, 508, 546, 586, 627, 670, 714, 759, 806, 854, 904, 955, 1007, 1061, 1116, 1173, 1231, 1290, 1351, 1413, 1477, 1542, 1608, 1676, 1745, 1816, 1888

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025648. - R. J. Mathar, Jul 06 2025

cp's OEIS Frontend

A025619 Numbers of form 4^i*7^j, with i, j >= 0.

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A131579 Period 10: repeat 0, 3, 6, 9, 2, 5, 8, 1, 4, 7.

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A025666 Exponent of 7 (value of j) in n-th number of form 4^i*7^j.

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A025722 Index of 7^n within sequence of numbers of form 4^i*7^j.

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