cp's OEIS Frontend

A162931 Irregular table which maps each partition of n counted in A162932 to a binary number (converted to decimal).

%I A162931 #8 May 30 2013 13:11:40
%S A162931 14,30,28,62,58,56,60,126,118,114,122,254,112,116,124,238,120,230,246,
%T A162931 510,226,234,250,478,224,228,236,242,252,462,494,1022
%N A162931 Irregular table which maps each partition of n counted in A162932 to a binary number (converted to decimal).
%C A162931 The table encodes each partition of n which satisfies the requirements of A162932 into a binary number with run lengths of 1 determined by the frequency of the parts. As many most-significant-bits are set as determined by the run length of the largest part, each run of 1 is terminated by a 0, and missing parts in the partition are represented by consecutive zeros. Each part in the partition and its frequency pick one member of A079946, and the full binary number is a concatenation of these bits. - _R. J. Mathar_, Jul 13 2012
%e A162931 For n=17, the A162932(17)=4 solutions are 2+2+2+2+3+3+3, 2+3+3+3+3+3, 2+3+4+4+4, and 2+5+5+5. These are represented here by
%e A162931 111011110=478 (3 threes give a run length of 3, and four 2's give a run length of 4),
%e A162931 11111010=250 (five 3's give a run length of 5 and one 2 gives a run length of 1),
%e A162931 11101010=234 (three 4's give a run length of 3, one 3 gives a run length of 1 and one 2 gives another run length of 1),
%e A162931 and 11100010=226 (three 5's give a run length of 3, missing 4 and 3 give two run lengths of zero, one 2 give one run length of 1),
%e A162931 then sorted into row 17. - _R. J. Mathar_, Jul 13 2012
%e A162931 A162932 begins 1 0 1 1 1 1 3 1 3 4 4 4 8 6 ... so the table begins
%e A162931 14
%e A162931 .
%e A162931 30
%e A162931 28
%e A162931 62
%e A162931 58
%e A162931 56,60,126
%e A162931 118
%e A162931 114,122,254
%e A162931 112,116,124,238
%e A162931 120,230,246,510
%e A162931 226,234,250,478
%e A162931 224,228,236,242,252,462,494,1022
%Y A162931 A162932 (number of entries per row). A079946
%K A162931 nonn,tabf,base,less
%O A162931 6,1
%A A162931 _Alford Arnold_, Jul 17 2009