A266295 - OEIS

%I #21 Mar 19 2023 13:36:18

%S 1,3,5,7,1,1,7,1,5,7,5,9,13,17,11,25,33,43,7,27,55,33,61,11,5,55,33,

%T 13,53,77,11,77,109,137,167,245,329,439,295,327,695,439,439,475,1,677,

%U 199,169,523,49,235,61,217,281,397,239,567,371,787

%N 2-free tetranacci sequence beginning 1,3,5,7.

%C For n>4, a(n) = (a(n-1) + a(n-2) + a(n-3) + a(n-4)) / 2^d, where 2^d is the largest power of 2 dividing a(n-1) + a(n-2) + a(n-3) + a(n-4). In other words, sum the previous four terms, then divide by two until the result is odd.

%D Alm, Herald, Miller, and Sexton, 2-Free Tetranacci Sequences, unpublished.

%H Jeremy F. Alm, <a href="/A266295/b266295.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (a(n-1) + a(n-2) + a(n-3) + a(n-4)) / 2^d, where 2^d is the largest power of 2 dividing a(n-1) + a(n-2) + a(n-3) + a(n-4).

%F a(n) = A000265(a(n-1) + a(n-2) + a(n-3) + a(n-4)). - _Michel Marcus_, Dec 29 2015

%t nxt[{a_, b_, c_, d_}] := {b, c, d, (a + b + c + d)/2^IntegerExponent[ a + b + c + d, 2]}; NestList[nxt,{1,3,5,7},60][[All,1]] (* _Harvey P. Dale_, Nov 09 2020 *)

%o (Python)

%o ### CREATES A b-FILE ###

%o def main():

%o     name = "b266295.txt"

%o     file = open(name, 'w')

%o     file.write('1' + ' ' + '1\n')

%o     file.write('2' + ' ' + '3\n')

%o     file.write('3' + ' ' + '5\n')

%o     file.write('4' + ' ' + '7\n')

%o     a, b, c, d = 1, 3, 5, 7

%o     for i in range(5,10001):

%o         x=a+b+c+d

%o         while x%2==0:

%o             x /= 2

%o         a, b, c, d = b, c, d, x

%o         file.write(str(i) + ' ' + str(int(d)) + '\n')

%o     file.close()

%o main()

%o (PARI) lista(nn) = {print1(x = 1, ", "); print1(y = 3, ", "); print1(z = 5, ", "); print1(t = 7, ", "); for (n=5, nn, tt = (x+y+z+t); tt /= 2^valuation(tt, 2); print1(tt, ", "); x=y; y=z; z=t; t=tt;);} \\ _Michel Marcus_, Dec 29 2015

%Y Cf. A000265, A232666, A233248, A233526.

%K nonn

%O 1,2

%A _Jeremy F. Alm_, Dec 28 2015