This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340441 #41 Jan 10 2021 12:46:10 %S A340441 3,13,11,3,205,43,57,5,3277,171,35,3641,7,52429,683,21,47,233017,19, %T A340441 838861,2731,3,79,99,14913081,23,13421773,10923,241,5,197,187, %U A340441 954437177,37,214748365,43691,7,61681,7,325,419,61083979321,39,3435973837,174763 %N A340441 Square array, read by ascending antidiagonals, where row n gives all odd solutions k > 1 and n > 0 to A000120(2*n+1) = A000120((2*n+1)*k), A000120 is the Hamming weight. %C A340441 Solutions to related equation A000120(k) = A000120(k*n) are A340351. %H A340441 Pontus von Brömssen, <a href="/A340441/b340441.txt">Antidiagonals n = 1..100, flattened</a> %F A340441 If 2*n = 2^j, then T(n, m) = (1+2^(j+2*j*m))/(2*n+1) for m > 0. In particular: %F A340441 T(1, m) = (1+2^(1+2*m))/3 = A007583(m), %F A340441 T(2, m) = (1+2^(2+4*m))/5 = A299960(m), %F A340441 T(4, m) = (1+2^(3+6*m))/9. %F A340441 The third row consists of all numbers of the form (1+2^(1+b*3)+2^(2+c*3))/7, where b and c are natural numbers >= 0 and b+c > 0. %F A340441 The seventh row consists of all numbers of the form (1+2^(1+b*2)+2^(2+c*2)+2^(3+d*2))/15 where b, c, and d are natural numbers >= 0 and b+c+d > 1. %e A340441 Five initial terms of rows 1-5 are listed below: %e A340441 1: 3, 11, 43, 171, 683, ... %e A340441 2: 13, 205, 3277, 52429, 838861, ... %e A340441 3: 3, 5, 7, 19, 23, ... %e A340441 4: 57, 3641, 233017, 14913081, 954437177, ... %e A340441 5: 35, 47, 99, 187, 419, ... %e A340441 T(3,4) = 19 because: (3*2+1) in binary is 111 and (3*2+1)*19 = 133 in binary is 10000101, both have 3 bits set to 1. %Y A340441 Cf. A000120, A340351, A340069. %Y A340441 Cf. A263132 (superset of 1st row), A007583 (1st row), A299960 (2nd row). %K A340441 nonn,base,tabl %O A340441 1,1 %A A340441 _Thomas Scheuerle_, Jan 07 2021 %E A340441 More terms from _Pontus von Brömssen_, Jan 08 2021