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 A327283 #25 Sep 23 2019 13:57:06 %S A327283 1,1,5,1,5,19,73,347,1,7,29,103,373,1631,1,5,23,133,1,11,1,5,19,65, %T A327283 451,1,7,53,1,5,31,125,503,2533,1,1,5,19,185,1,7,29,151,581,2255, %U A327283 10861,1,5,23,85,287,925 %N A327283 Irregular triangle T(n,k) read by rows: "residual summands" in reduced Collatz sequences (see Comments for definition and explanation). %C A327283 Let R_s be the reduced Collatz sequence (cf. A259663) starting with s and let R_s(k), k >= 0 be the k-th term in R_s. Then R_(2n-1)(k) = (3^k*(2n-1) + T(n,k))/2^j, where j is the total number of halving steps from R_(2n-1)(0) to R_(2n-1)(k). T(n,k) is defined here as the "residual summand". %C A327283 The sequence without duplicates is a permutation of A116641. %F A327283 T(n,k) = 2^j*R_(2n-1)(k) - 3^k*(2n-1), as defined in Comments. %F A327283 T(n,1) = 1; for k>1: T(n,k) = 3*T(n,k-1) + 2^i, where i is the total number of halving steps from R_(2n-1)(0) to R_(2n-1)(k-1). %e A327283 Triangle starts: %e A327283 1; %e A327283 1, 5; %e A327283 1; %e A327283 1, 5, 19, 73, 347; %e A327283 1, 7, 29, 103, 373, 1631; %e A327283 1, 5, 23, 133; %e A327283 1, 11; %e A327283 1, 5, 19, 65, 451; %e A327283 1, 7, 53; %e A327283 1, 5, 31, 125, 503, 2533; %e A327283 1; %e A327283 1, 5, 19, 185; %e A327283 1, 7, 29, 151, 581, 2255, 10861; %e A327283 ... %e A327283 T(5,4)=103 because R_9(4) = 13; the number of halving steps from R_9(0) to R_9(4) is 6, and 13 = (81*9 + 103)/64. %Y A327283 Cf. A116623, A116641, A259663. %K A327283 nonn,tabf %O A327283 1,3 %A A327283 _Bob Selcoe_, Sep 15 2019