A059872 - OEIS

%I #14 Oct 13 2022 18:26:26

%S 1,3,5,13,21,46,51,52,78,83,84,175,181,205,210,303,309,333,338,390,

%T 392,639,698,726,728,737,822,824,846,851,852,903,905,1143,1145,1197,

%U 1202,1226,1232,1311,1322,1328,1350,1352,1409,1562,1571,1572,1601,2539,2540

%N Solutions to the equation given in A059871, encoded as binary vectors and converted to decimal.

%C The rows of this table have lengths given by A059871.

%C In binary encodings, the least significant bit (bit-0) stands for the factor of 1, the next bit (bit-1) stands for the factor of 2, bit-2 for the factor of 3, bit-3 for the factor of 5, etc., each bit being 0 if the corresponding factor is -1 and 1 if it is +1 (or +2 if the bit is the most significant bit of the code of odd length).

%C E.g. we have 2 = 2*1 -> 1 in binary, 3 = 1*2 + 1*1 -> 11 in binary, 5 = 2*3 - 1*2 + 1*1 -> 101 in binary, 7 = 1*5 + 1*3 - 1*2 + 1*1 -> 1101 in binary, 11 = 2*7 - 1*5 + 1*3 - 1*2 + 1*1 -> 10101 in binary. Function bin_prime_sum given in A059876 maps such encodings back to primes.

%H Sean A. Irvine, <a href="/A059872/b059872.txt">Table of n, a(n) for n = 1..10000</a>

%e Rows are:

%e   1;

%e   3;

%e   5;

%e   13;

%e   21;

%e   46,51,52;

%e   78,83,84;

%e   175,181,205,210;

%e   ...

%p map(op, primesums_primes_mult(16)); # primesums_primes_mult given in A059871.

%Y Cf. A059871, A059873, A059874, A059875, A059876.

%K nonn,tabf,base

%O 1,2

%A _Antti Karttunen_, Feb 05 2001