

A331745


Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A323901(i) = A323901(j) for all i, j.


5



1, 2, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 8, 5, 9, 2, 10, 6, 11, 4, 12, 7, 13, 3, 14, 8, 15, 5, 16, 9, 17, 2, 18, 10, 19, 6, 20, 11, 21, 4, 22, 12, 23, 7, 24, 13, 25, 3, 26, 14, 27, 8, 28, 15, 29, 5, 30, 16, 31, 9, 32, 17, 33, 2, 34, 18, 35, 10, 36, 19, 37, 6, 38, 20, 39, 11, 24, 21, 40, 4, 41, 22, 42, 12, 43, 23, 44, 7, 45, 24, 46, 13, 47, 25, 48, 3, 49, 26, 50, 14, 51, 27, 52, 8, 45
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OFFSET

0,2


COMMENTS

Restricted growth sequence transform of the ordered pair [A278222(n), A323901(n)].


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n
Index entries for sequences related to Stern's sequences


FORMULA

a(2^n) = 2 for all n >= 0.


PROG

(PARI)
\\ Needs also code from A323901.
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 };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278222(n) = A046523(A005940(1+n));
Aux331745(n) = [A278222(n), A323901(n)];
v331745 = rgs_transform(vector(1+up_to, n, Aux331745(n1)));
A331745(n) = v331745[1+n];


CROSSREFS

Cf. A278222, A323901.
Cf. also A324400, A286622, A318310, A324389, A331744, A331746.
Sequence in context: A205378 A323889 A286378 * A103391 A331743 A178804
Adjacent sequences: A331742 A331743 A331744 * A331746 A331747 A331748


KEYWORD

nonn


AUTHOR

Antti Karttunen, Feb 04 2020


STATUS

approved



