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 A068052 Start from 1, shift one left and sum mod 2 (bitwise-XOR) to get 3 (11 in binary), then shift two steps left and XOR to get 15 (1111 in binary), then three steps and XOR to get 119 (1110111 in binary), then four steps and so on. 10
 1, 3, 15, 119, 1799, 59367, 3743271, 481693095, 123123509927, 62989418816679, 64491023022979239, 132015402419352060071, 540829047855347718631591, 4430403202865824763042320551, 72583450474242118015031400337575 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = each row of A053632 reduced mod 2 and interpreted as a binary number. LINKS Antti Karttunen, Table of n, a(n) for n = 0..64 FORMULA a(0) = 1; for n > 0, a(n) = a(n-1) XOR (2^n)*a(n-1), where XOR is bitwise-XOR (A003987). a(n) = A248663(A285101(n)) = A048675(A285102(n)). A000120(a(n)) = A285103(n). [Number of ones in binary representation.] A080791(a(n)) = A285105(n). [Number of nonleading zeros.] MAPLE with(gfun, seriestolist); [seq(foo(map(`mod`, seriestolist(series(mul(1+(z^i), i=1..n), z, binomial(n+1, 2)+1)), 2)), n=0..20)]; foo := proc(a) local i; add(a[i]*2^(i-1), i=1..nops(a)); end; PROG (Scheme, with memoization-macro definec) (definec (A068052 n) (if (zero? n) 1 (A003987bi (A068052 (- n 1)) (* (A000079 n) (A068052 (- n 1)))))) ;; A003987bi implements bitwise-XOR (A003987). (PARI) a(n) = if(n<1, 1, bitxor(a(n - 1), 2^n*a(n - 1))); \\ Indranil Ghosh, Apr 15 2017, after formula by Antti Karttunen CROSSREFS Same sequence shown in binary: A068053. Cf. A000120, A003987, A028362 (using + instead of XOR), A048675, A053632, A080791, A248663, A285101, A285102, A285103, A285105. Sequence in context: A145161 A121422 A060639 * A068859 A006454 A225115 Adjacent sequences:  A068049 A068050 A068051 * A068053 A068054 A068055 KEYWORD nonn,base AUTHOR Antti Karttunen, Feb 13 2002 EXTENSIONS Formulas added by Antti Karttunen, Apr 15 2017 STATUS approved

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Last modified June 17 05:41 EDT 2021. Contains 345080 sequences. (Running on oeis4.)