A064743 -id:A064743 - cp's OEIS frontend

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

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

A064740 Smallest controlling prime when A064413(n) is computed.

Original entry on oeis.org

2, 2, 2, 3, 3, 3, 2, 2, 5, 5, 3, 2, 7, 7, 3, 2, 2, 2, 11, 11, 3, 3, 5, 5, 7, 2, 13, 13, 3, 2, 2, 17, 17, 3, 2, 19, 19, 3, 5, 2, 2, 23, 23, 3, 2, 2, 2, 2, 7, 7, 3, 5, 5, 5, 2, 29, 29, 3, 2, 31, 31, 3, 2, 2, 2, 37, 37, 3, 3, 2, 2, 2, 41, 41, 3, 3, 7, 11, 2, 43, 43, 3, 5, 5, 5, 2, 2, 47, 47, 3, 2, 7

Offset: 2

N. J. A. Sloane, Oct 18 2001

Michael De Vlieger, Table of n, a(n) for n = 2..10000
Michael De Vlieger, Mathematica code based on Lagarias-Rains-Sloane 2002, efficiently generates this sequence.
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446; arXiv:math/0204011 [math.NT], 2002.
Index entries for sequences related to EKG sequence

Cf. A064413, A064741, A064742, A064743, A020639, A073734.

a(n) = A020639(A073734(n)). - Michael De Vlieger, Dec 10 2021

More terms from David Wasserman, Aug 05 2002

A064742 Total number of primes (with multiplicity) dividing A064413(n).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 18 2001

nonn

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

Sum of "digits" of A064743.

Cf. A001222, A064413.

terms = 105;
ekg[s_] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
EKG = Nest[ekg, {1, 2}, terms-2];
PrimeOmega /@ EKG (* Jean-François Alcover, Sep 02 2018, after Robert G. Wilson v in A064413 *)

a(n) = A001222(A064413(n)). - Michel Marcus, Aug 21 2023

More terms from Vladeta Jovovic, Oct 20 2001

A064744 A064413(n) written in base of primes, read from right to left, written as n-th row of a table.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 19 2001

			Triangle begins:
  0;
  1;
  2;
  1,1;
  1,0;
  2,0;
  1,2;
  3;
  ...

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

A064741(n) gives length of n-th row. See A064743 for another version. See A064301 for rightmost column.

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

cp's OEIS Frontend

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

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A064740 Smallest controlling prime when A064413(n) is computed.

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A064742 Total number of primes (with multiplicity) dividing A064413(n).

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A064744 A064413(n) written in base of primes, read from right to left, written as n-th row of a table.

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A353728 A115510(n) written in base 2.

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Python