A366254 -id:A366254 - cp's OEIS frontend

A366261 The least number with the same prime signature as A366260, where A366260 is Doudna sequence permuted by May code.

1, 2, 4, 2, 4, 2, 6, 8, 16, 2, 6, 12, 6, 8, 4, 12, 24, 2, 6, 12, 6, 12, 6, 30, 24, 32, 4, 12, 36, 12, 16, 8, 16, 2, 6, 12, 6, 12, 6, 30, 24, 48, 6, 30, 60, 30, 24, 12, 60, 48, 4, 12, 36, 12, 36, 12, 60, 72, 64, 8, 24, 72, 24, 32, 64, 2, 6, 12, 6, 12, 6, 30, 24, 48, 6, 30, 60, 30, 24, 12, 60, 120, 6, 30, 60, 30, 60

Offset: 0

Antti Karttunen, Oct 05 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A005940, A046523, A303767, A366260, A366262 (rgs-transform).

Cf. also A278219, A278222.

A046523(n) = { my(f=vecsort(factor(n)[,2],,4),p);prod(i=1,#f,(p=nextprime(p+1))^f[i]) }
A366261(n) = A046523(A366260(n)); \\ Needs also the program given in A366260.

a(n) = A046523(A366260(n)).
a(n) = A278222(A303767(n)).
A001222(a(n)) = A366254(n).

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

Original entry on oeis.org

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];

cp's OEIS Frontend

A366261 The least number with the same prime signature as A366260, where A366260 is Doudna sequence permuted by May code.

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