A365432 -id:A365432 - cp's OEIS frontend

A365431 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364502(i) = A364502(j) for all i, j >= 1, where A364502(n) is the denominator of n / A005940(n).

1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 2, 2, 1, 6, 3, 7, 1, 8, 4, 9, 1, 10, 5, 5, 2, 11, 2, 12, 1, 13, 6, 14, 3, 15, 7, 7, 1, 16, 8, 17, 4, 18, 9, 19, 1, 20, 10, 10, 5, 21, 5, 9, 2, 22, 11, 23, 2, 24, 12, 25, 1, 26, 13, 27, 6, 28, 14, 29, 3, 30, 15, 6, 7, 5, 7, 31, 1, 32, 16, 33, 8, 16, 17, 17, 4, 34, 18, 35, 9, 36, 19, 12, 1

Offset: 1

Antti Karttunen, Sep 07 2023

Restricted growth sequence transform of A364502, or equally, of A365432.
For all i, j: A003602(i) = A003602(j) => a(i) = a(j).
Compare to the scatter plots of A365393 and A365715.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A005940, A364502, A365432.

Cf. also A365393, A365715 (analogous sequence for Doudna variant D(3)).

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 };
A364502(n) = { my(u=A005940(n)); (u / gcd(n, u)); };
v365431 = rgs_transform(vector(up_to,n,A364502(n)));
A365431(n) = v365431[n];

A365430 a(n) = A156552(gcd(n, A005940(n))), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 0, 7, 0, 9, 0, 11, 0, 1, 2, 15, 0, 1, 0, 19, 8, 1, 0, 23, 0, 1, 2, 3, 0, 5, 0, 31, 0, 1, 0, 3, 0, 1, 2, 39, 0, 17, 0, 3, 4, 1, 0, 47, 0, 1, 2, 3, 0, 5, 4, 7, 0, 1, 0, 11, 0, 1, 6, 63, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 10, 3, 16, 5, 0, 79, 0, 1, 0, 35, 4, 1, 2, 7, 0, 9, 8, 3, 0, 1, 4, 95, 0, 1, 34, 3

Offset: 1

Antti Karttunen, Sep 07 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A005940, A364500, A341520, A365432.

A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A364500(n) = { my(orgn=n,p=2,rl=0,z=1); n--; while(n, if(!(n%2), p=nextprime(1+p), rl++; if(1==(n%4), z *= p^min(rl,valuation(orgn,p)); rl=0)); n>>=1); (z); };
A365430(n) = A156552(A364500(n));

a(n) = A156552(A364500(n)).

For all n >= 1, a(n) <= n-1 and A341520(a(n), A365432(n)) = n-1.

cp's OEIS Frontend

A365431 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364502(i) = A364502(j) for all i, j >= 1, where A364502(n) is the denominator of n / A005940(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI