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 A341907 #17 Jun 08 2021 02:33:38
%S A341907 0,1,0,0,1,0,1,1,1,0,0,2,2,1,0,1,1,3,3,1,0,0,2,4,4,4,1,0,1,2,5,9,5,5,
%T A341907 1,0,0,3,6,10,16,6,6,1,0,1,1,7,12,17,25,7,7,1,0,0,2,8,13,20,26,36,8,8,
%U A341907 1,0,1,2,9,27,21,30,37,49,9,9,1,0,0,3,10,28,64,31,42,50,64,10,10,1,0
%N A341907 T(n, k) is the result of replacing 2^e with k^e in the binary expansion of n; square array T(n, k) read by antidiagonals upwards, n, k >= 0.
%C A341907 For any n >= 0, the n-th row, k -> T(n, k), corresponds to a polynomial in k with coefficients in {0, 1}.
%C A341907 For any k > 1, the k-th column, n -> T(n, k), corresponds to sums of distinct powers of k.
%H A341907 Rémy Sigrist, <a href="/A341907/b341907.txt">Table of n, a(n) for n = 0..10010</a>
%H A341907 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A341907 T(n, n) = A104258(n).
%F A341907 T(n, 0) = A000035(n).
%F A341907 T(n, 1) = A000120(n).
%F A341907 T(n, 2) = n.
%F A341907 T(n, 3) = A005836(n).
%F A341907 T(n, 4) = A000695(n).
%F A341907 T(n, 5) = A033042(n).
%F A341907 T(n, 6) = A033043(n).
%F A341907 T(n, 7) = A033044(n).
%F A341907 T(n, 8) = A033045(n).
%F A341907 T(n, 9) = A033046(n).
%F A341907 T(n, 10) = A007088(n).
%F A341907 T(n, 11) = A033047(n).
%F A341907 T(n, 12) = A033048(n).
%F A341907 T(n, 13) = A033049(n).
%F A341907 T(0, k) = 0.
%F A341907 T(1, k) = 1.
%F A341907 T(2, k) = k.
%F A341907 T(3, k) = k + 1.
%F A341907 T(4, k) = k^2.
%F A341907 T(5, k) = k^2 + 1 = A002522(k).
%F A341907 T(6, k) = k^2 + k = A002378(k).
%F A341907 T(7, k) = k^2 + k + 1 = A002061(k).
%F A341907 T(8, k) = k^3.
%F A341907 T(9, k) = k^3 + 1 = A001093(k).
%F A341907 T(10, k) = k^3 + k = A034262(k).
%F A341907 T(11, k) = k^3 + k + 1 = A071568(k).
%F A341907 T(12, k) = k^3 + k^2 = A011379(k).
%F A341907 T(13, k) = k^3 + k^2 + 1 = A098547(k).
%F A341907 T(14, k) = k^3 + k^2 + k = A027444(k).
%F A341907 T(15, k) = k^3 + k^2 + k + 1 = A053698(k).
%F A341907 T(16, k) = k^4 = A000583(k).
%F A341907 T(17, k) = k^4 + 1 = A002523(k).
%F A341907 T(m + n, k) = T(m, k) + T(n, k) when m AND n = 0 (where AND denotes the bitwise AND operator).
%e A341907 Array T(n, k) begins:
%e A341907 n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12
%e A341907 ---+-------------------------------------------------------------
%e A341907 0| 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A341907 1| 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A341907 2| 0 1 2 3 4 5 6 7 8 9 10 11 12
%e A341907 3| 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A341907 4| 0 1 4 9 16 25 36 49 64 81 100 121 144
%e A341907 5| 1 2 5 10 17 26 37 50 65 82 101 122 145
%e A341907 6| 0 2 6 12 20 30 42 56 72 90 110 132 156
%e A341907 7| 1 3 7 13 21 31 43 57 73 91 111 133 157
%e A341907 8| 0 1 8 27 64 125 216 343 512 729 1000 1331 1728
%e A341907 9| 1 2 9 28 65 126 217 344 513 730 1001 1332 1729
%e A341907 10| 0 2 10 30 68 130 222 350 520 738 1010 1342 1740
%e A341907 11| 1 3 11 31 69 131 223 351 521 739 1011 1343 1741
%e A341907 12| 0 2 12 36 80 150 252 392 576 810 1100 1452 1872
%o A341907 (PARI) T(n,k) = { my (v=0, e); while (n, n-=2^e=valuation(n,2); v+=k^e); v }
%Y A341907 See A342707 for a similar sequence.
%Y A341907 Cf. A000035, A000120, A000583, A000695, A001093, A002061, A002378, A002522, A002523, A005836, A007088, A011379, A027444, A033042, A033043, A033044, A033045, A033046, A033047, A033048, A033049, A034262, A053698, A071568, A098547, A104258.
%K A341907 nonn,tabl,base
%O A341907 0,12
%A A341907 _Rémy Sigrist_, Jun 04 2021