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 A037095 "Sloping binary representation" of powers of 3 (A000244), slope = -1. 7
 1, 1, 3, 1, 3, 9, 11, 17, 19, 25, 123, 65, 195, 169, 171, 753, 435, 249, 2267, 4065, 8163, 841, 843, 31313, 29651, 39769, 38331, 30081, 160643, 49769, 53867, 563377, 700659, 1611961, 760731, 1207073, 5668771, 5566345, 11844619, 8699025, 10386067, 55868313 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2000 FORMULA a(n) = A339601(A000244(n)). - Antti Karttunen, Dec 09 2020 EXAMPLE When powers of 3 are written in binary (see A004656), under each other as: 000000000001 (1) 000000000011 (3) 000000001001 (9) 000000011011 (27) 000001010001 (81) 000011110011 (243) 001011011001 (729) 100010001011 (2187) and one collects their bits from the column-0 to NW-direction (from the least to the most significant end), one gets 1 (1), 01 (1), 011 (3), 0001 (1), 00011 (3), 001001 (9), etc. (See A105033 for similar transformation done on nonnegative integers, A001477). MAPLE A037095:= n-> add(bit_n(3^(n-i), i)*(2^i), i=0..n): bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2): seq(A037095(n), n=0..41); # second Maple program: b:= proc(n) option remember; `if`(n=0, 1, (p-> expand((p-(p mod 2))*x/2)+3^n)(b(n-1))) end: a:= n-> subs(x=2, b(n) mod 2): seq(a(n), n=0..42); # Alois P. Heinz, Dec 10 2020 PROG (PARI) A339601(n) = { my(m=1, s=0); while(n>=m, s += bitand(m, n); m <<= 1; n \= 3); (s); }; A037095(n) = A339601(3^n); \\ Antti Karttunen, Dec 09 2020 (PARI) BINSLOPE(f) = n -> sum(i=0, n, bitand(2^(n-i), f(i))); \\ General transformation for these kinds of sequences. A037095 = BINSLOPE(n -> 3^n); \\ And its application to A000244. - Antti Karttunen, Dec 09 2020 CROSSREFS Cf. A105033, A000244, A037093, A037094, A037096, A037097, A339601. Sequence in context: A265307 A133579 A088442 * A160654 A146436 A058842 Adjacent sequences: A037092 A037093 A037094 * A037096 A037097 A037098 KEYWORD nonn,base AUTHOR Antti Karttunen, Jan 28 1999. Entry revised Dec 29 2007. EXTENSIONS More terms from Sean A. Irvine, Dec 08 2020 STATUS approved

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Last modified April 17 13:32 EDT 2024. Contains 371764 sequences. (Running on oeis4.)