A064741 -id:A064741 - cp's OEIS frontend

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

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

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

Original entry on oeis.org

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

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.

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.

A304733 The largest prime factor of the n-th term of EKG-sequence: a(n) = A006530(A064413(n)).

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 3, 2, 5, 5, 5, 3, 7, 7, 7, 3, 2, 5, 11, 11, 11, 3, 5, 5, 7, 7, 13, 13, 13, 3, 2, 17, 17, 17, 7, 19, 19, 19, 5, 5, 11, 23, 23, 23, 3, 5, 13, 3, 7, 7, 7, 5, 11, 13, 7, 29, 29, 29, 11, 31, 31, 31, 3, 2, 17, 37, 37, 37, 5, 13, 19, 5, 41, 41, 41, 3, 7, 11, 11, 43, 43, 43, 5, 17, 19, 5, 23, 47, 47, 47, 3, 7, 13, 13, 17, 11, 7, 3, 53, 53, 53, 19

Offset: 1

Antti Karttunen, May 18 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to EKG sequence

Cf. A006530, A064413, A064741, A304734.

Cf. also A251103.

ekGrapher[s_List] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
FactorInteger[#][[-1, 1]]& /@ Nest[ekGrapher, {1, 2}, 100] (* Jean-François Alcover, Dec 20 2021, after Robert G. Wilson v in A064413 *)

A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A304733(n) = A006530(A064413(n)); \\ Needs also an implementation of A064413.

a(n) = A006530(A064413(n)).

A304734 Ordinal transform of the largest prime factor of the n-th term of EKG-sequence.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, May 18 2018

Ordinal transform of A304733(n) = A006530(A064413(n)).

Antti Karttunen, Table of n, a(n) for n = 1..20090
Index entries for sequences related to EKG sequence

Cf. A006530, A064413, A064741, A304733.

Cf. also A078899.

terms = 105;
ekGrapher[s_List] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
A304733 = FactorInteger[#][[-1, 1]]& /@ Nest[ekGrapher, {1, 2}, terms];
b[_] = 0;
a[n_] := a[n] = With[{t = A304733[[n]]}, b[t] = b[t]+1];
Array[a, terms] (* Jean-François Alcover, Dec 20 2021, after Robert G. Wilson v in A064413 *)

A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A304733(n) = A006530(A064413(n)); \\ Needs also code for A064413.
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
v304734 = ordinal_transform(vector(65539,n,A304733(n)));
A304734(n) = v304734[n];

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

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A064301 Rightmost column of A064744; 2-adic valuation of the 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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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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A304733 The largest prime factor of the n-th term of EKG-sequence: a(n) = A006530(A064413(n)).

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A304734 Ordinal transform of the largest prime factor of the n-th term of EKG-sequence.

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