A064301 -id:A064301 - cp's OEIS frontend

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

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.

A304735 a(n) = A048675(A064413(n)).

Original entry on oeis.org

0, 1, 2, 3, 2, 4, 4, 3, 5, 4, 6, 5, 9, 8, 10, 5, 4, 6, 17, 16, 18, 6, 7, 8, 12, 10, 33, 32, 34, 6, 5, 65, 64, 66, 11, 129, 128, 130, 8, 7, 18, 257, 256, 258, 6, 9, 34, 7, 11, 16, 12, 8, 20, 36, 13, 513, 512, 514, 19, 1025, 1024, 1026, 7, 6, 66, 2049, 2048, 2050, 10, 35, 130, 8, 4097, 4096, 4098, 8, 12, 24, 19, 8193, 8192, 8194, 9, 68, 132, 10

Offset: 1

Antti Karttunen, May 18 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..1024
Index entries for sequences related to EKG sequence

Cf. A048675, A064301, A064413, A304736.

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.

a(n) = A048675(A064413(n)).

A304737 Restricted growth sequence transform of A278222(A064413(n)).

Original entry on oeis.org

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

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 A064413(n), the n-th term of EKG-sequence. Compare to the scatter plot of A286622.

Cf. A064301, A064413, A278222, A286622.

Cf. also A304738.

\\ 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; };
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));
v304737 = rgs_transform(vector(65539,n,A278222(A064413(n))));
A304737(n) = v304737[n];

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];

cp's OEIS Frontend

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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A304735 a(n) = A048675(A064413(n)).

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A304737 Restricted growth sequence transform of A278222(A064413(n)).

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

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