A292260 -id:A292260 - cp's OEIS frontend

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

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];

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)).

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)).

A305295 Binary encoding of 1-digits in ternary representation of A245612(n).

Original entry on oeis.org

1, 0, 2, 2, 6, 7, 0, 3, 14, 4, 12, 1, 2, 0, 4, 0, 30, 37, 0, 5, 26, 28, 0, 1, 6, 17, 8, 14, 10, 9, 4, 1, 62, 16, 72, 103, 2, 90, 8, 0, 54, 25, 60, 33, 2, 32, 0, 19, 14, 40, 32, 40, 18, 11, 24, 0, 22, 18, 16, 9, 10, 8, 0, 4, 126, 333, 36, 305, 146, 4, 204, 331, 6, 147, 176, 44, 18, 225, 8, 121, 110, 214, 48, 203, 122, 6, 64, 78, 6, 1

Offset: 0

Antti Karttunen, May 31 2018

Cf. A245612, A289813, A305296 (rgs-transform).
Cf. also A292260, A291763.
Cf. also A304759, A304760.

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))));
A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A305295(n) = A289813(A245612(n));

cp's OEIS Frontend

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

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A292250 Binary encoding of 0-digits in ternary representation 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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A305295 Binary encoding of 1-digits in ternary representation of A245612(n).

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PARI