A358230 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A007949(i) = A007949(j) and A046523(i) = A046523(j), for all i, j, where A007814 and A007949 give the 2-adic and 3-adic valuation, and A046523 gives the prime signature of its argument.

1, 2, 3, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 9, 11, 12, 5, 13, 5, 14, 11, 9, 5, 15, 16, 9, 17, 14, 5, 18, 5, 19, 11, 9, 20, 21, 5, 9, 11, 22, 5, 18, 5, 14, 23, 9, 5, 24, 16, 25, 11, 14, 5, 26, 20, 22, 11, 9, 5, 27, 5, 9, 23, 28, 20, 18, 5, 14, 11, 29, 5, 30, 5, 9, 31, 14, 20, 18, 5, 32, 33, 9, 5, 27, 20, 9, 11, 22, 5, 34, 20, 14, 11, 9, 20, 35, 5, 25, 23, 36, 5, 18, 5, 22, 37

Offset: 1

Author

Antti Karttunen, Dec 01 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of the triple [A007814(n), A007949(n), A046523(n)].

For all i, j:

A305900(i) = A305900(j) => a(i) = a(j),

a(i) = a(j) => A305891(i) = A305891(j),

a(i) = a(j) => A305893(i) = A305893(j),

a(i) = a(j) => A322026(i) = A322026(j) => A072078(i) = A072078(j),

a(i) = a(j) => A065333(i) = A065333(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A007814, A007949, A046523, A065333, A072078, A305891, A305893, A322026.

Cf. also A358747.

Programs

PARI

up_to = 100000;
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; };
A007814(n) = valuation(n,2);
A007949(n) = valuation(n,3);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
v358230 = rgs_transform(vector(up_to, n, [A007814(n), A007949(n), A046523(n)]));
A358230(n) = v358230[n];