A292261 -id:A292261 - 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.

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.

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)).

A292262 Number of trailing 2-digits in ternary representation of A245612(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 12 2017

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

Cf. A007814, A007949, A245612, A291763, A292261 (even bisection subtracted by one).

Cf. also A292242, A292252.

(define (A292262 n) (A007949 (+ 1 (A245612 n))))
(define (A292262 n) (A007814 (+ 1 (A291763 n))))
(define (A292262 n) (cond ((<= n 1) n) ((odd? n) 0) (else (+ 1 (A292261 (/ n 2))))))

a(n) = A007949(1+A245612(n)).
a(n) = A007814(1+A291763(n)).
a(0) = 0, a(1) = 1, after which a(2n) = 1 + A292261(n/2), a(2n+1) = 0.

A305297 Restricted growth sequence transform of A292260, formed from 0-digits in ternary representation of A245612(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 4, 1, 1, 3, 4, 2, 1, 5, 6, 7, 8, 2, 4, 8, 1, 9, 1, 2, 8, 10, 1, 1, 1, 11, 12, 1, 5, 13, 14, 15, 6, 4, 1, 7, 8, 16, 7, 9, 1, 17, 18, 19, 1, 8, 8, 3, 6, 17, 20, 4, 1, 17, 4, 3, 1, 21, 22, 23, 24, 25, 4, 26, 27, 1, 24, 28, 29, 9, 5, 4, 5, 13, 10, 30, 1, 31, 14, 13, 6, 32, 33, 6, 34, 15, 18, 4, 1, 35, 6, 31, 36, 1, 30, 36, 1, 37

Offset: 0

Antti Karttunen, May 31 2018

nonn

For all i, j: a(i) = a(j) => A292261(i) = A292261(j).

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

Cf. A291770, A292260, A245612, A292261.
Cf. also A305296, A305298.
Cf. also A304750.

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;
A254049(n) = A048673((2*n)-1);
A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
A291770(n) = { my(s=0, b=1, d); while(n>2, if(!(n%3), s += b); b <<= 1; n \= 3); (s); };
A292260(n) = A291770(A245612(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; };
v305297 = rgs_transform(vector(65538,n,A292260(n-1)));
A305297(n) = v305297[1+n];

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

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

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

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A292262 Number of trailing 2-digits in ternary representation of A245612(n).

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A305297 Restricted growth sequence transform of A292260, formed from 0-digits in ternary representation of A245612(n).

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