

A292383


Base2 expansion of a(n) encodes the steps where numbers of the form 4k+3 are encountered when map x > A252463(x) is iterated down to 1, starting from x=n.


25



0, 0, 1, 0, 2, 2, 5, 0, 0, 4, 11, 4, 22, 10, 5, 0, 44, 0, 89, 8, 8, 22, 179, 8, 0, 44, 1, 20, 358, 10, 717, 0, 20, 88, 11, 0, 1434, 178, 45, 16, 2868, 16, 5737, 44, 8, 358, 11475, 16, 0, 0, 89, 88, 22950, 2, 17, 40, 176, 716, 45901, 20, 91802, 1434, 17, 0, 40, 40, 183605, 176, 356, 22, 367211, 0, 734422, 2868, 1, 356, 22, 90, 1468845, 32, 0, 5736, 2937691, 32
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OFFSET

1,5


LINKS



FORMULA

a(1) = 0; for n > 1, a(n) = 2*a(A252463(n)) + [n ≡ 3 (mod 4)], where the last part of the formula is Iverson bracket, giving 1 only if n is of the form 4k+3, and 0 otherwise.
Other identities. For n >= 1:
a(2n) = 2*a(n).


EXAMPLE

For n = 3, the starting value is of the form 4k+3, after which follows A252463(3) = 2, and A252463(2) = 1, the end point of iteration, and neither 2 nor 1 is of the form 4k+3, thus a(3) = 1*(2^0) + 0*(2^1) + 0*(2^2) = 1.
For n = 5, the starting value is not of the form 4k+3, after which follows A252463(5) = 3 (which is), continuing as before as 3 > 2 > 1, thus a(5) = 0*(2^0) + 1*(2^1) + 0*(2^2) + 0*(2^3) = 2.
For n = 10, the starting value is not of the form 4k+3, after which follows A252463(10) = 5 (also not 4k+3), and then A252463(5) = 3 (which is), continuing as before as 3 > 2 > 1, thus a(10) = 0*(2^0) + + 0*(2^1) + 1*(2^2) + 0*(2^3) + 0*(2^4) = 4.


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] == 3, 1, 0], 2], {n, 84}] (* Michael De Vlieger, Sep 21 2017 *)


PROG

(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]1)); factorback(f)};


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



