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A336153
Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A009194(i) = A009194(j), for all i, j >= 1.
3
1, 2, 3, 2, 1, 4, 5, 2, 1, 6, 3, 7, 1, 6, 8, 2, 1, 9, 3, 6, 1, 6, 5, 10, 1, 6, 3, 11, 1, 4, 12, 2, 13, 6, 3, 2, 1, 6, 5, 14, 1, 4, 3, 7, 13, 6, 15, 7, 1, 2, 16, 6, 1, 4, 5, 17, 1, 6, 3, 10, 1, 6, 18, 2, 1, 4, 3, 6, 13, 6, 5, 9, 1, 6, 3, 7, 1, 4, 15, 6, 1, 6, 3, 11, 1, 6, 19, 7, 1, 20, 21, 7, 1, 6, 22, 10, 1, 2, 16, 2, 1, 4, 5, 6, 13
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of the ordered pair [A007814(1+n), A009194(n)]. Note that A007814(1+n) gives the number of trailing 1-bits in the binary expansion of n.
For all i, j: A324400(i) = A324400(j) => a(i) = a(j).
LINKS
PROG
(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);
A009194(n) = gcd(n, sigma(n));
Aux336153(n) = [A007814(1+n), A009194(n)];
v336153 = rgs_transform(vector(up_to, n, Aux336153(n)));
A336153(n) = v336153[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 11 2020
STATUS
approved