A366261 -id:A366261 - cp's OEIS frontend

A366262 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366261(i) = A366261(j) for all i, j >= 0.

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

Offset: 0

Antti Karttunen, Oct 05 2023

nonn

Restricted growth sequence transform of A366261.

For all i, j >= 0: a(i) = a(j) => A366254(i) = A366254(j).

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

Cf. A366254, A366260, A366261.

Cf. also A286602, A286619, A286622.

up_to = 65537;
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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A209229(n) = (n && !bitand(n,n-1));
A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); };
A303767(n) = if(!n,n,if(A209229(n),n+A303767(n-1),A053644(n)+A303767(n-A053644(n)-1)));
A366260(n) = A005940(1+A303767(n));
A366261(n) = A046523(A366260(n));
v366262 = rgs_transform(vector(1+up_to,n,A366261(n-1)));
A366262(n) = v366262[1+n];

A366260 Doudna sequence permuted by May code: a(n) = A005940(1+A303767(n)).

Original entry on oeis.org

1, 2, 4, 3, 9, 5, 6, 8, 16, 7, 10, 12, 15, 27, 25, 18, 54, 11, 14, 20, 21, 45, 35, 30, 24, 32, 49, 50, 36, 75, 81, 125, 625, 13, 22, 28, 33, 63, 55, 42, 40, 48, 77, 70, 60, 105, 135, 175, 90, 162, 121, 98, 100, 147, 225, 245, 150, 72, 64, 343, 250, 108, 375, 243, 729, 17, 26, 44, 39, 99, 65, 66, 56, 80, 91, 110

Offset: 0

Antti Karttunen, Oct 05 2023

nonn

Cf. A005940, A303767, A366261, A366262.

Cf. also A243353, A366263.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A209229(n) = (n && !bitand(n,n-1));
A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
A303767(n) = if(!n,n,if(A209229(n),n+A303767(n-1),A053644(n)+A303767(n-A053644(n)-1)));
A366260(n) = A005940(1+A303767(n));

A366254 Binary weight of May code (A303767).

Original entry on oeis.org

0, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 3, 2, 3, 2, 3, 4, 1, 2, 3, 2, 3, 2, 3, 4, 5, 2, 3, 4, 3, 4, 3, 4, 1, 2, 3, 2, 3, 2, 3, 4, 5, 2, 3, 4, 3, 4, 3, 4, 5, 2, 3, 4, 3, 4, 3, 4, 5, 6, 3, 4, 5, 4, 5, 6, 1, 2, 3, 2, 3, 2, 3, 4, 5, 2, 3, 4, 3, 4, 3, 4, 5, 2, 3, 4, 3, 4, 3, 4, 5, 6, 3, 4, 5, 4, 5, 4, 5, 2, 3, 4, 3, 4, 3, 4, 5

Offset: 0

Antti Karttunen, Oct 05 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A000120, A001221, A001222, A064547, A303760, A303767, A303771, A366255, A366261.

Cf. also A005811, A234022.

A209229(n) = (n && !bitand(n,n-1));
A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
A303767(n) = if(!n,n,if(A209229(n),n+A303767(n-1),A053644(n)+A303767(n-A053644(n)-1)));
A366254(n) = hammingweight(A303767(n));

a(n) = A000120(A303767(n)).
a(n) = A001221(A303760(n)) = A001222(A303760(n)) = A001222(A366261(n)).
a(n) = A064547(A303771(n)).

A366279 The least number with same prime signature as A366275, where A366275(n) = A163511(A057889(n)).

Original entry on oeis.org

1, 2, 4, 2, 8, 4, 6, 2, 16, 8, 12, 6, 12, 4, 6, 2, 32, 16, 24, 12, 36, 12, 30, 6, 24, 8, 12, 6, 12, 4, 6, 2, 64, 32, 48, 24, 72, 36, 60, 12, 72, 24, 60, 30, 60, 12, 30, 6, 48, 16, 24, 12, 36, 12, 30, 6, 24, 8, 12, 6, 12, 4, 6, 2, 128, 64, 96, 48, 144, 72, 120, 24, 216, 72, 180, 60, 180, 36, 60, 12, 144, 48, 120, 60

Offset: 0

Antti Karttunen, Oct 06 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16383

Cf. A046523, A057889, A163511, A278531, A366275, A366280 (rgs-transform).

Cf. also A286601, A366261.

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A366275(n) = A163511(A057889(n));
A366279(n) = A046523(A366275(n));

a(n) = A046523(A366275(n)) = A046523(A163511(A057889(n))).

a(n) = A278531(A057889(n)).

cp's OEIS Frontend

A366262 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366261(i) = A366261(j) for all i, j >= 0.

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A366260 Doudna sequence permuted by May code: a(n) = A005940(1+A303767(n)).

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A366254 Binary weight of May code (A303767).

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A366279 The least number with same prime signature as A366275, where A366275(n) = A163511(A057889(n)).

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