

A036566


Numbers of form 7^i*8^j with i, j >= 0, sorted.


4



1, 7, 8, 49, 56, 64, 343, 392, 448, 512, 2401, 2744, 3136, 3584, 4096, 16807, 19208, 21952, 25088, 28672, 32768, 117649, 134456, 153664, 175616, 200704, 229376, 262144, 823543, 941192, 1075648, 1229312, 1404928, 1605632, 1835008, 2097152
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OFFSET

1,2


COMMENTS

Could be rearranged as a triangle of numbers in which ith row is {7^(ij)*8^j, 0<=j<=i}; i >= 0. (This would produce a different sequence, of course).
The sum of the reciprocals of the terms of this sequence is equal to 4/3. Brief proof: as gcd(7, 8) = 1, 1 + 1/7 + 1/8 + 1/49 + 1/56 + 1/64 + 1/343 + ... = (Sum_{k>=0} 1/7^k) * (Sum_{m>=0} 1/8^m) = (1/(11/7)) * (1/(11/8)) = (7/(71)) * (8/(81)) = 4/3.  Bernard Schott, Oct 24 2019


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Robert Sedgewick, Analysis of shellsort and related algorithms, Fourth European Symposium on Algorithms, Barcelona, September, 1996.


MAPLE

N:= 10^7: # for all terms <= N
sort([seq(seq(7^i*8^j, j=0..floor(log[8](N/7^i))), i=0..floor(log[7](N)))]); # Robert Israel, Oct 24 2019


CROSSREFS

Sequence in context: A270009 A033044 A025630 * A116554 A038274 A201919
Adjacent sequences: A036563 A036564 A036565 * A036567 A036568 A036569


KEYWORD

easy,nonn


AUTHOR

David W. Wilson


STATUS

approved



