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A266295 2-free tetranacci sequence beginning 1,3,5,7. 1
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, 13, 53, 77, 11, 77, 109, 137, 167, 245, 329, 439, 295, 327, 695, 439, 439, 475, 1, 677, 199, 169, 523, 49, 235, 61, 217, 281, 397, 239, 567, 371, 787 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

REFERENCES

Alm, Herald, Miller, and Sexton, 2-Free Tetranacci Sequences, unpublished.

LINKS

Jeremy F. Alm, Table of n, a(n) for n = 1..10000

FORMULA

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).

a(n) = A000265(a(n-1) + a(n-2) + a(n-3) + a(n-4)). - Michel Marcus, Dec 29 2015

PROG

(Python)

### CREATES A b-FILE ###

def main():

    name = "b266295.txt"

    file = open(name, 'w')

    file.write('1' + ' ' + '1\n')

    file.write('2' + ' ' + '3\n')

    file.write('3' + ' ' + '5\n')

    file.write('4' + ' ' + '7\n')

    a, b, c, d = 1, 3, 5, 7

    for i in xrange(5, 10001):

        x=a+b+c+d

        while x%2==0:

            x /= 2

        a, b, c, d = b, c, d, x

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

    file.close()

main()

(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

CROSSREFS

Cf. A000265, A232666, A233248, A233526.

Sequence in context: A031057 A133069 A192327 * A172049 A021032 A212120

Adjacent sequences:  A266292 A266293 A266294 * A266296 A266297 A266298

KEYWORD

nonn

AUTHOR

Jeremy F. Alm, Dec 28 2015

STATUS

approved

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Last modified June 16 15:38 EDT 2019. Contains 324153 sequences. (Running on oeis4.)