A366262 -id:A366262 - cp's OEIS frontend

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

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));

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

Original entry on oeis.org

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).

A366280 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366279(i) = A366279(j) for all i, j >= 0.

Original entry on oeis.org

1, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 5, 7, 3, 5, 2, 8, 6, 9, 7, 10, 7, 11, 5, 9, 4, 7, 5, 7, 3, 5, 2, 12, 8, 13, 9, 14, 10, 15, 7, 14, 9, 15, 11, 15, 7, 11, 5, 13, 6, 9, 7, 10, 7, 11, 5, 9, 4, 7, 5, 7, 3, 5, 2, 16, 12, 17, 13, 18, 14, 19, 9, 20, 14, 21, 15, 21, 10, 15, 7, 18, 13, 19, 15, 21, 15, 22, 11, 19, 9, 15, 11, 15

Offset: 0

Antti Karttunen, Oct 06 2023

Restricted growth sequence transform of A366279.

For all i, j >= 0, a(i) = a(j) => A290251(i) = A290251(j).

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

Cf. A046523, A057889, A163511, A278531, A290251, A366275, A366279.

Cf. also A286531, A286602, A366262.

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; };
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));
v366280 = rgs_transform(vector(1+up_to,n,A366279(n-1)));
A366280(n) = v366280[1+n];

cp's OEIS Frontend

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

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

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A366280 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366279(i) = A366279(j) for all i, j >= 0.

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