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 A287874 Concatenate prime factorization as in A080670, but write everything in binary. 8
 1, 10, 11, 1010, 101, 1011, 111, 1011, 1110, 10101, 1011, 101011, 1101, 10111, 11101, 10100, 10001, 101110, 10011, 1010101, 11111, 101011, 10111, 101111, 10110, 101101, 1111, 1010111, 11101, 1011101, 11111, 10101, 111011, 1010001, 101111, 10101110, 100101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As in A080670 the prime factorization of n is written as p1^e1*...*pN^eN (except for exponents eK = 1 which are omitted), with all factors and exponents in binary (cf. A007088). Then "^" and "*" signs are dropped and all binary digits are concatenated. See A230625 for the terms written in base 10, and for further information (fixed points, trajectories). LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A007088(A230625(n)). - R. J. Mathar, Jun 16 2017 EXAMPLE a(1) = 1 by convention. a(2) = 10 (= 2 written in binary). a(4) = 1010 = concatenate(10,10), since 4 = 2^2 = 10 ^ 10. a(6) = 1011 = concatenate(10,11), since 6 = 2*3 = 10 * 11. a(8) = 1011 = concatenate(10,11), since 8 = 2^3 = 10 ^ 11. MAPLE f:= proc(n) local F, L, i;     F:= map(op, subs(1=NULL, sort(ifactors(n), (a, b) -> a < b)));     F:= map(convert, F, binary);     L:= map(length, F);     L:= ListTools:-Reverse(ListTools:-PartialSums(ListTools:-Reverse(L)));     add(F[i]*10^L[i+1], i=1..nops(F)-1)+F[-1]; end proc: f(1):= 1: map(f, [\$1..100]); # Robert Israel, Jun 20 2017 PROG (PARI) A287874(n)=if(n>1, fromdigits(concat(apply(binary, select(t->t>1, concat(Col(factor(n))~)))), 10), 1) \\ M. F. Hasler, Jun 21 2017 (Python) from sympy import factorint def a(n):     f=factorint(n)     return 1 if n==1 else int("".join([bin(i)[2:] + bin(f[i])[2:] if f[i]!=1 else bin(i)[2:] for i in f])) print [a(n) for n in xrange(1, 101)] # Indranil Ghosh, Jun 23 2017 CROSSREFS Cf. A080670, A230625, A230626, A230627, A287875. Sequence in context: A318089 A109280 A181756 * A064841 A286200 A286411 Adjacent sequences:  A287871 A287872 A287873 * A287875 A287876 A287877 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Jun 15 2017 EXTENSIONS Edited by M. F. Hasler, Jun 21 2017 STATUS approved

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Last modified October 14 14:39 EDT 2019. Contains 328019 sequences. (Running on oeis4.)