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 A351995 #18 Aug 26 2025 10:03:48
%S A351995 0,1,0,1,1,0,2,2,1,0,1,3,4,1,0,2,4,5,8,1,0,2,5,16,9,16,1,0,3,6,17,64,
%T A351995 17,32,1,0,1,7,20,65,256,33,64,1,0,2,8,21,72,257,1024,65,128,1,0,2,9,
%U A351995 64,73,272,1025,4096,129,256,1,0,3,10,65,512,273,1056,4097,16384,257,512,1,0
%N A351995 Square array A(n, k), n, k >= 0, read by antidiagonals upwards; A(n, k) = Sum_{ i >= 0 } b_i * 2^(k*i) where n = Sum_{ i >= 0 } b_i * 2^i.
%C A351995 In other words, in binary expansion of n, replace 2^i by 2^(k*i).
%H A351995 Rémy Sigrist, <a href="/A351995/b351995.txt">Table of n, a(n) for n = 0..10010</a>
%H A351995 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A351995 A(A(n, k), k') = A(n, k*k') for k, k' > 0.
%F A351995 A(n, 0) = A000120(n).
%F A351995 A(n, 1) = n.
%F A351995 A(n, 2) = A000695(n).
%F A351995 A(n, 3) = A033045(n).
%F A351995 A(n, 4) = A033052(n).
%F A351995 A(0, k) = 0.
%F A351995 A(1, k) = 1.
%F A351995 A(2, k) = 2^k.
%F A351995 A(3, k) = 2^k + 1.
%e A351995 Square array A(n, k) begins:
%e A351995 n\k| 0 1 2 3 4 5 6 7 8 9 10
%e A351995 ------------------------------------------------------------------
%e A351995 0| 0 0 0 0 0 0 0 0 0 0 0
%e A351995 1| 1 1 1 1 1 1 1 1 1 1 1
%e A351995 2| 1 2 4 8 16 32 64 128 256 512 1024
%e A351995 3| 2 3 5 9 17 33 65 129 257 513 1025
%e A351995 4| 1 4 16 64 256 1024 4096 16384 65536 262144 1048576
%e A351995 5| 2 5 17 65 257 1025 4097 16385 65537 262145 1048577
%e A351995 6| 2 6 20 72 272 1056 4160 16512 65792 262656 1049600
%e A351995 7| 3 7 21 73 273 1057 4161 16513 65793 262657 1049601
%t A351995 A351995[n_, k_] := If[n <= 1, n, Total[2^(k*(Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]] - 1))]];
%t A351995 Table[A351995[n - k, k], {n, 0, 15}, {k, 0, n}] (* _Paolo Xausa_, Aug 26 2025 *)
%o A351995 (PARI) A(n,k) = { my (v=0, e); while (n, n-=2^e=valuation(n, 2); v+=2^(k*e)); v }
%Y A351995 Cf. A000120, A000695, A033045, A033052, A352001.
%K A351995 nonn,base,tabl,changed
%O A351995 0,7
%A A351995 _Rémy Sigrist_, Feb 27 2022