A292240 -id:A292240 - cp's OEIS frontend

A304750 Restricted growth sequence transform of A292240(n), formed from 0-digits in ternary representation of A254103(n).

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

Offset: 0

Antti Karttunen, May 30 2018

nonn

For all i, j: a(i) = a(j) => A292241(i) = A292241(j).

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A254103, A291770, A292240.

Cf. also A292241, A304740, A304746.

A254103(n) = if(!n,n,if(!(n%2),(3*A254103(n/2))-1,(3*(1+A254103((n-1)/2)))\2));
A291770(n) = { my(s=0, b=1, d); while(n>2, if(!(n%3), s += b); b <<= 1; n \= 3); (s); };
A292240(n) = A291770(A254103(n));
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; };
v304750 = rgs_transform(vector(65538,n,A292240(n-1)));
A304750(n) = v304750[1+n];

A292241 The 3-adic valuation of A254103(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 12 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384

One less than the even bisection of A292242.
Cf. A007814, A007949, A254103, A292240.
Cf. also A292251, A292261.

a(n) = A007814(1+A292240(n)).
a(n) = A007949(A254103(n)).
For n >= 1, a(n) = A007949(3*A254103(n)) - 1.
For n >= 1, a(n) = A292242(2n)-1.

A292250 Binary encoding of 0-digits in ternary representation of A048673(n).

Original entry on oeis.org

0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 3, 0, 2, 2, 1, 4, 6, 2, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 5, 6, 1, 4, 1, 4, 0, 8, 0, 14, 1, 4, 12, 0, 7, 0, 4, 2, 1, 0, 5, 8, 2, 0, 4, 2, 4, 0, 4, 6, 5, 0, 5, 8, 3, 12, 2, 4, 2, 8, 0, 4, 1, 8, 3, 2, 1, 16, 16, 2, 3, 28, 0, 0, 1, 8, 0, 26, 8, 0, 9, 0, 15, 0, 1, 10, 14, 4, 0, 4, 7, 0, 4, 12, 6, 16, 5, 6, 8, 0, 2, 10, 9, 4

Offset: 1

Antti Karttunen, Sep 12 2017

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

Cf. A048673, A291759, A291770, A292251, A292252.

Cf. also A292240, A292260.

Map[FromDigits[IntegerDigits[#, 3] /. k_ /; k < 3 :> If[k == 0, 1, 0], 2] &, Table[(Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n, {n, 116}]] (* Michael De Vlieger, Sep 12 2017 *)

a(n) = A291770(A048673(n)).

A292260 Binary encoding of 0-digits in ternary representation of A245612(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 0, 3, 2, 1, 0, 16, 8, 10, 4, 1, 2, 4, 0, 12, 0, 1, 4, 6, 0, 0, 0, 41, 34, 0, 16, 33, 22, 11, 8, 2, 0, 10, 4, 21, 10, 12, 0, 5, 26, 23, 0, 4, 4, 3, 8, 5, 14, 2, 0, 5, 2, 3, 0, 146, 80, 132, 68, 43, 2, 180, 32, 0, 68, 81, 44, 12, 16, 2, 16, 33, 6, 48, 0, 9, 22, 33, 8, 54, 40, 8, 20, 11, 26, 2, 0, 126, 8, 9, 52, 0, 48, 52, 0

Offset: 0

Antti Karttunen, Sep 12 2017

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A245612, A291763, A291770, A292261, A292262.

Cf. also A292240, A292260.

a(n) = A291770(A245612(n)).

cp's OEIS Frontend

A304750 Restricted growth sequence transform of A292240(n), formed from 0-digits in ternary representation of A254103(n).

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A292241 The 3-adic valuation of A254103(n).

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A292250 Binary encoding of 0-digits in ternary representation of A048673(n).

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A292260 Binary encoding of 0-digits in ternary representation of A245612(n).

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