A292241 -id:A292241 - cp's OEIS frontend

A292251 The 3-adic valuation of A048673(n).

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

Offset: 1

Antti Karttunen, Sep 12 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

One less than the even bisection of A292252.
Cf. A007814, A007949, A048673, A292250.
Cf. also A292241, A292261.

IntegerExponent[#, 3] & /@ Table[(Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n, {n, 120}] (* Michael De Vlieger, Sep 12 2017 *)

a(n) = A007814(1+A292250(n)).
a(n) = A007949(A048673(n)).
a(n) = A007949(3*A048673(n)) - 1.
a(n) = A292252(2n)-1.

A292261 The 3-adic valuation of A245612(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 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 A292262.
Cf. A007814, A007949, A245612, A292260.
Cf. also A292241, A292251.

a(n) = A007814(1+A292260(n)).
a(n) = A007949(A245612(n)).
For n >= 1, a(n) = A007949(3*A245612(n)) - 1.
For n >= 1, a(n) = A292262(2n)-1.

A292240 Binary encoding of 0-digits in ternary representation of A254103(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 1, 0, 3, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 4, 3, 2, 1, 0, 3, 2, 1, 0, 7, 6, 0, 0, 3, 2, 4, 0, 0, 0, 1, 8, 0, 0, 6, 4, 4, 4, 2, 0, 8, 8, 6, 4, 4, 4, 5, 0, 0, 0, 1, 12, 3, 2, 0, 0, 8, 8, 9, 4, 11, 10, 0, 0, 3, 2, 4, 0, 0, 0, 2, 16, 3, 2, 1, 0, 15, 14, 0, 8, 11, 10, 1, 8, 7, 6, 5, 0, 19, 18, 1, 16, 15, 14, 13, 8, 11

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. A254103, A291760, A291770, A292241, A292242.

Cf. also A292250, A292260.

a(n) = A291770(A254103(n)).

A292242 Number of trailing 2-digits in ternary representation of A254103(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 12 2017

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

Cf. A007814, A007949, A254103, A291760, A292241 (even bisection subtracted by one).

Cf. also A292252, A292262.

(define (A292242 n) (A007949 (+ 1 (A254103 n))))
(define (A292242 n) (A007814 (+ 1 (A291760 n))))
(define (A292242 n) (cond ((zero? n) n) ((odd? n) 0) (else (+ 1 (A292241 (/ n 2))))))

a(n) = A007949(1+A254103(n)).
a(n) = A007814(1+A291760(n)).
a(0) = 0, after which, a(2n) = 1 + A292241(n/2), a(2n+1) = 0.

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

Original entry on oeis.org

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];

cp's OEIS Frontend

A292251 The 3-adic valuation of A048673(n).

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A292261 The 3-adic valuation of A245612(n).

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A292240 Binary encoding of 0-digits in ternary representation of A254103(n).

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A292242 Number of trailing 2-digits in ternary representation of A254103(n).

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

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