A292262 -id:A292262 - cp's OEIS frontend

A292252 Number of trailing 2-digits in ternary representation of A048673(n).

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

Offset: 1

Antti Karttunen, Sep 12 2017

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

Cf. A007814, A007949, A048673, A291759, A292251 (even bisection subtracted by one).

Cf. also A292242, A292262.

If[First@ # == 2, Length@ #, 0] &@ Last@ Split@ IntegerDigits[#, 3] & /@ Table[(Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n, {n, 120}] (* Michael De Vlieger, Sep 12 2017 *)

(define (A292252 n) (A007949 (+ 1 (A048673 n))))
(define (A292252 n) (A007814 (+ 1 (A291759 n))))
(define (A292252 n) (if (odd? n) 0 (+ 1 (A292251 (/ n 2)))))

a(n) = A007949(1+A048673(n)).
a(n) = A007814(1+A291759(n)).
a(2n) = 1 + A292251(n/2), a(2n+1) = 0.

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)).

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.

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.

A305298 Restricted growth sequence transform of A291763, formed from 2-digits in ternary representation of A291763(n).

Original entry on oeis.org

1, 2, 2, 1, 2, 1, 3, 1, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 8, 12, 9, 13, 8, 14, 1, 2, 1, 3, 8, 2, 15, 16, 17, 18, 7, 19, 20, 2, 21, 3, 22, 23, 9, 16, 1, 24, 25, 6, 1, 12, 11, 3, 26, 2, 4, 2, 7, 6, 8, 6, 1, 2, 27, 28, 29, 30, 31, 32, 1, 33, 34, 35, 36, 37, 25, 38, 7, 2, 4, 39, 7, 6, 40, 30, 11, 32, 41, 42, 43, 30, 22, 2, 4, 19, 1, 44, 45, 13, 43, 46, 4

Offset: 0

Antti Karttunen, May 31 2018

nonn

For all i, j: a(i) = a(j) => A292262(i) = A292262(j).

For all i, j: a(i) = a(j) => A305432(i) = A305432(j).

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

Cf. A245612, A289814, A291763, A292262, A305432.
Cf. also A305296, A305297.
Cf. also A304746, A304748.

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))));
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291763(n) = A289814(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; };
v305298 = rgs_transform(vector(65538,n,A291763(n-1)));
A305298(n) = v305298[1+n];

cp's OEIS Frontend

A292252 Number of trailing 2-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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A292261 The 3-adic valuation of A245612(n).

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

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A305298 Restricted growth sequence transform of A291763, formed from 2-digits in ternary representation of A291763(n).

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