A286601 -id:A286601 - cp's OEIS frontend

A286602 Restricted growth sequence transform of A286601.

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

Offset: 0

Antti Karttunen, Jun 04 2017

The scatter plot looks complex.

Antti Karttunen, Table of n, a(n) for n = 0..65535

Cf. A193231, A234022.

Cf. A286581, A286589, A286597, A286599, A286600, A286601, A286617, A286619, A286622 for similarly formed sequences.

A366263 Doudna sequence permuted by Blue code: a(n) = A005940(1+A193231(n)).

Original entry on oeis.org

1, 2, 4, 3, 6, 5, 9, 8, 16, 27, 25, 18, 15, 12, 10, 7, 14, 11, 21, 20, 35, 30, 24, 45, 81, 32, 54, 125, 36, 75, 49, 50, 100, 147, 121, 98, 225, 72, 150, 245, 625, 162, 64, 243, 250, 343, 375, 108, 33, 28, 22, 13, 40, 63, 55, 42, 90, 175, 135, 48, 77, 70, 60, 105, 210, 385, 315, 120, 143, 154, 140, 231, 525, 180

Offset: 0

Antti Karttunen, Oct 06 2023

Cf. A005940, A193231, A234022, A268389, A277818, A286601, A286602, A332450, A366264 (inverse map).

Cf. also A365810, A366260, A366275.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) };
A366263(n) = A005940(1+A193231(n));

a(n) = A332450(A005940(1+n)).
For all n >= 0, A001222(a(n)) = A234022(n) and A046523(a(n)) = A286601(n).
For all n >= 1, A055396(a(n)) = A277818(n) = 1+A268389(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

A286602 Restricted growth sequence transform of A286601.

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A366263 Doudna sequence permuted by Blue code: a(n) = A005940(1+A193231(n)).

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

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