A064744 -id:A064744 - cp's OEIS frontend

A064301 Rightmost column of A064744; 2-adic valuation of the EKG-sequence.

0, 1, 2, 1, 0, 0, 2, 3, 1, 0, 0, 1, 1, 0, 0, 3, 4, 2, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 5, 1, 0, 0, 1, 1, 0, 0, 0, 3, 2, 1, 0, 0, 4, 1, 2, 1, 3, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 3, 6, 2, 1, 0, 0, 0, 1, 2, 4, 1, 0, 0, 0, 2, 0, 3, 1, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 5, 1, 0, 3, 1, 0, 0, 2, 1, 0, 0, 1, 1, 4, 2

Offset: 1

N. J. A. Sloane, Oct 20 2001

nonn

Exponent of highest power of 2 dividing A064413(n).

Antti Karttunen, Table of n, a(n) for n = 1..65539
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, arXiv:math/0204011 [math.NT], 2002.
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446.
Index entries for sequences related to EKG sequence
Index entries for sequences related to Recamán's sequence

Cf. A064413, A064741, A064744, A304735, A304737.

IntegerExponent[#, 2] & /@ Nest[Append[#, Block[{k = 3}, While[Or[MemberQ[#, k], GCD[#[[-1]], k] == 1], k++]; k]] &, {1, 2}, 105] (* Michael De Vlieger, May 22 2018 *)

A064301(n) = valuation(A064413(n),2); \\ Needs also code from A064413. - Antti Karttunen, May 18 2018

More terms from Vladeta Jovovic, Oct 21 2001

An alternative description added to name by Antti Karttunen, May 18 2018

A064741 Length of A064743(n); Index of the largest prime factor of the n-th term of EKG-sequence.

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 2, 1, 3, 3, 3, 2, 4, 4, 4, 2, 1, 3, 5, 5, 5, 2, 3, 3, 4, 4, 6, 6, 6, 2, 1, 7, 7, 7, 4, 8, 8, 8, 3, 3, 5, 9, 9, 9, 2, 3, 6, 2, 4, 4, 4, 3, 5, 6, 4, 10, 10, 10, 5, 11, 11, 11, 2, 1, 7, 12, 12, 12, 3, 6, 8, 3, 13, 13, 13, 2, 4, 5, 5, 14, 14, 14, 3, 7, 8, 3, 9, 15, 15, 15, 2, 4, 6, 6, 7, 5, 4, 2, 16, 16, 16, 8, 5, 4, 10

Offset: 1

N. J. A. Sloane, Oct 18 2001

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65539
Index entries for sequences related to EKG sequence

Length of n-th row of table in A064744.

Cf. A061395, A064413, A304733, A304734 (ordinal transform).

PrimePi@ FactorInteger[#][[-1, 1]] & /@ Nest[Append[#, Block[{k = 3}, While[Or[MemberQ[#, k], GCD[#[[-1]], k] == 1], k++]; k]] &, {1, 2}, 103] (* Michael De Vlieger, May 22 2018 *)

A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
A064741(n) = A061395(A064413(n)); \\ Needs also code for A064413.

a(n) = A061395(A064413(n)) = A000720(A304733(n)). - Antti Karttunen, May 18 2018

Offset corrected to 1, terms a(42) .. a(46) [that were terms a(41) .. a(45)] also corrected, more terms and alternative description added by Antti Karttunen, May 18 2018

A064743 A064413(n) written in base of primes, read from right to left, written as a string.

Original entry on oeis.org

0, 1, 2, 11, 10, 20, 12, 3, 101, 100, 110, 21, 1001, 1000, 1010, 13, 4, 102, 10001, 10000, 10010, 30, 111, 200, 1100, 1002, 100001, 100000, 100010, 22, 5, 1000001, 1000000, 1000010, 1011, 10000001, 10000000, 10000010, 120, 103, 10002

Offset: 1

N. J. A. Sloane, Oct 18 2001

nonn

			A064413(12) = 18 = 3^2*2^1, so a(12) = 21.

J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446.
Index entries for sequences related to EKG sequence

Of course this "string" representation will not work once A064413 reaches 1024. See also A064744.

Cf. A064740, A064741, A064742, A064744.

A353728 A115510(n) written in base 2.

Original entry on oeis.org

1, 11, 10, 110, 100, 101, 111, 1001, 1000, 1010, 1011, 1100, 1101, 1110, 1111, 10001, 10000, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, 100001, 100000, 100010, 100011, 100100, 100101, 100110, 100111, 101000, 101001, 101010, 101011, 101100, 101101, 101110, 101111

Offset: 1

N. J. A. Sloane, May 13 2022

Cf. A115510; A064413, A064743, A064744.

from itertools import islice
def A353728_gen(): # generator of terms
    yield 1
    l1, s, b = 1, 2, set()
    while True:
        i = s
        while True:
            if i & l1 and not i in b:
                yield int(bin(i)[2:])
                l1 = i
                b.add(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break
            i += 1
A353728_list = list(islice(A353728_gen(),30)) # Chai Wah Wu, May 13 2022

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A064301 Rightmost column of A064744; 2-adic valuation of the EKG-sequence.

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A064741 Length of A064743(n); Index of the largest prime factor of the n-th term of EKG-sequence.

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A064743 A064413(n) written in base of primes, read from right to left, written as a string.

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A353728 A115510(n) written in base 2.

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