A304735 -id:A304735 - 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

A304736 Restricted growth sequence transform of A048675(A064413(n)).

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 5, 4, 6, 5, 7, 6, 8, 9, 10, 6, 5, 7, 11, 12, 13, 7, 14, 9, 15, 10, 16, 17, 18, 7, 6, 19, 20, 21, 22, 23, 24, 25, 9, 14, 13, 26, 27, 28, 7, 8, 18, 14, 22, 12, 15, 9, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 14, 7, 21, 39, 40, 41, 10, 42, 25, 9, 43, 44, 45, 9, 15, 46, 35, 47, 48, 49, 8, 50, 51, 10, 28, 52, 53, 54, 14, 11, 55, 42, 56, 29, 57, 9

Offset: 1

Antti Karttunen, May 18 2018

nonn

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

Cf. A048675, A064413, A304735.

Cf. also A064301, A304113.

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A304735(n) = A048675(A064413(n)); \\ Needs also code for A064413.
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
v304736 = rgs_transform(vector(65539,n,A304735(n)));
A304736(n) = v304736[n];

A304739 a(n) = A056239(A064413(n)).

Original entry on oeis.org

0, 1, 2, 3, 2, 4, 4, 3, 4, 3, 5, 5, 5, 4, 6, 5, 4, 5, 6, 5, 7, 6, 6, 6, 7, 6, 7, 6, 8, 6, 5, 8, 7, 9, 7, 9, 8, 10, 7, 6, 7, 10, 9, 11, 6, 7, 8, 7, 7, 8, 8, 7, 8, 9, 8, 11, 10, 12, 8, 12, 11, 13, 7, 6, 9, 13, 12, 14, 8, 9, 10, 7, 14, 13, 15, 8, 8, 9, 8, 15, 14, 16, 8, 10, 11, 8, 11, 16, 15, 17, 7, 9, 10, 9, 10, 9, 9, 8, 17, 16, 18, 11, 9, 8, 12

Offset: 1

Antti Karttunen, May 19 2018

nonn

For visualizing of the EKG-sequence, A064413.

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

Cf. A056239, A064413, A304735.

A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
A304739(n) = A056239(A064413(n)); \\ Needs also code for A064413.

a(n) = A056239(A064413(n)).

cp's OEIS Frontend

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

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A304736 Restricted growth sequence transform of A048675(A064413(n)).

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A304739 a(n) = A056239(A064413(n)).

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