A304737 -id:A304737 - 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

A304738 Restricted growth sequence transform of A278222(A048673(n)).

Original entry on oeis.org

1, 1, 2, 3, 1, 1, 2, 4, 5, 5, 4, 6, 3, 3, 3, 7, 3, 5, 2, 1, 4, 3, 8, 3, 5, 5, 9, 5, 1, 10, 5, 11, 3, 6, 6, 6, 7, 5, 10, 12, 5, 10, 2, 13, 5, 5, 14, 15, 11, 7, 2, 10, 8, 11, 6, 16, 6, 11, 17, 11, 3, 4, 7, 18, 8, 5, 3, 10, 7, 6, 7, 16, 3, 17, 19, 5, 3, 1, 7, 6, 20, 3, 10, 17, 5, 6, 6, 5, 5, 6, 11, 5, 20, 3, 7, 5, 14, 15, 10, 21, 5, 11, 14, 13, 5

Offset: 1

Antti Karttunen, May 18 2018

nonn

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A048673(n). Compare to the scatter plot of A286622.

Cf. A003961, A048673, A278222, A286622.

Cf. also A286243, A304101, A304737.

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
v304738 = rgs_transform(vector(65539,n,A278222(A048673(n))));
A304738(n) = v304738[n];

cp's OEIS Frontend

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

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