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 A292380 Base-2 expansion of a(n) encodes the steps where multiples of 4 are encountered when map x -> A252463(x) is iterated down to 1, starting from x=n. 7
 0, 0, 0, 1, 0, 0, 0, 3, 2, 0, 0, 1, 0, 0, 0, 7, 0, 4, 0, 1, 0, 0, 0, 3, 4, 0, 6, 1, 0, 0, 0, 15, 0, 0, 0, 9, 0, 0, 0, 3, 0, 0, 0, 1, 2, 0, 0, 7, 8, 8, 0, 1, 0, 12, 0, 3, 0, 0, 0, 1, 0, 0, 2, 31, 0, 0, 0, 1, 0, 0, 0, 19, 0, 0, 8, 1, 0, 0, 0, 7, 14, 0, 0, 1, 0, 0, 0, 3, 0, 4, 0, 1, 0, 0, 0, 15, 0, 16, 2, 17, 0, 0, 0, 3, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = A048735(A156552(n)). a(n) = A292370(A292384(n)). Other identities. For n >= 1: a(n) AND A292382(n) = 0, where AND is a bitwise-AND (A004198). a(n) + A292382(n) = A156552(n). A000120(a(n)) + A000120(A292382(n)) = A001222(n). A000035(a(n)) = A121262(n). EXAMPLE For n = 4, the starting value is a multiple of four, after which follows A252463(4) = 2, and A252463(2) = 1, the end point of iteration, and neither 2 nor 1 is a multiple of four, thus a(4) = 1*(2^0) + 0*(2^1) + 0*(2^2) = 1. For n = 8, the starting value is a multiple of four, after which follows A252463(8) = 4 (also a multiple), continuing as before as 4 -> 2 -> 1, thus a(8) = 1*(2^0) + 1*(2^1) + 0*(2^2) + 0*(2^3) = 3. For n = 9, the starting value is not a multiple of four, after which follows A252463(9) = 4 (which is), continuing as before as 4 -> 2 -> 1, thus a(9) = 0*(2^0) + 1*(2^1) + 0*(2^2) + 0*(2^3) = 2. MATHEMATICA Table[FromDigits[Reverse@ NestWhileList[Function[k, Which[k == 1, 1, EvenQ@ k, k/2, True, Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ k]], n, # > 1 &] /. k_ /; IntegerQ@ k :> If[Mod[k, 4] == 0, 1, 0], 2], {n, 105}] (* Michael De Vlieger, Sep 21 2017 *) PROG (Scheme) (define (A292380 n) (A292370 (A292384 n))) (Python) from sympy.core.cache import cacheit from sympy.ntheory.factor_ import digits from sympy import factorint, prevprime from operator import mul from functools import reduce def a292370(n):     k=digits(n, 4)[1:]     return 0 if n==0 else int("".join(['1' if i==0 else '0' for i in k]), 2) def a064989(n):     f=factorint(n)     return 1 if n==1 else reduce(mul, [1 if i==2 else prevprime(i)**f[i] for i in f]) def a252463(n): return 1 if n==1 else n//2 if n%2==0 else a064989(n) @cacheit def a292384(n): return 1 if n==1 else 4*a292384(a252463(n)) + n%4 def a(n): return a292370(a292384(n)) print([a(n) for n in range(1, 111)]) # Indranil Ghosh, Sep 21 2017 (PARI) a(n) = my(m=factor(n), k=-1, ret=0); for(i=1, matsize(m)[1], ret += bitneg(0, m[i, 2]-1) << (primepi(m[i, 1])+k); k+=m[i, 2]); ret; \\ Kevin Ryde, Dec 11 2020 CROSSREFS Cf. A005940, A048735, A156552, A292370, A292381, A292382, A292383, A292384. Sequence in context: A206590 A206825 A336551 * A242165 A231724 A214851 Adjacent sequences:  A292377 A292378 A292379 * A292381 A292382 A292383 KEYWORD nonn,base AUTHOR Antti Karttunen, Sep 15 2017 STATUS approved

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Last modified November 27 07:28 EST 2021. Contains 349365 sequences. (Running on oeis4.)