A340680 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A292251(i) = A292251(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Feb 11 2021

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A007814(1+n), A292251(n)], where the first element is the 2-adic valuation of 1+n (i.e., the number of trailing 1-digits in the base-2 representation of n), and the latter element is the 3-adic valuation of A048673(n).

For all i, j: a(i) = a(j) => A341345(i) = A341345(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A007814, A048673, A292251, A341345.

Cf. also A322026.

Programs

PARI

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; };
A007814(n) = valuation(n,2);
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A292251(n) = valuation(A048673(n),3);
Aux340680(n) = [A007814(1+n), A292251(n)];
v340680 = rgs_transform(vector(up_to, n, Aux340680(n)));
A340680(n) = v340680[n];

Formula

a(2n) = 2.