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A324533
Lexicographically earliest positive sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A278219(i) = A278219(j), for all i, j >= 0.
2
1, 2, 3, 4, 3, 5, 6, 7, 3, 8, 9, 10, 6, 11, 12, 13, 3, 11, 14, 15, 9, 16, 17, 18, 6, 19, 17, 20, 12, 15, 21, 22, 3, 23, 24, 25, 14, 26, 27, 28, 9, 29, 30, 31, 17, 32, 33, 34, 6, 35, 27, 36, 17, 37, 38, 39, 12, 40, 33, 39, 21, 25, 41, 42, 3, 15, 43, 39, 24, 44, 45, 46, 14, 47, 48, 49, 27, 50, 51, 46, 9, 52, 48, 53, 30, 54, 55, 56, 17, 57, 58, 59, 33, 60, 61, 62, 6
OFFSET
0,2
COMMENTS
Restricted growth sequence transform of the ordered pair [A002487(n), A278219(n)].
FORMULA
For n >= 1, a(2^n) = 3.
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; };
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
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
A003188(n) = bitxor(n, n>>1);
Aux324533(n) = [A002487(n), A278219(n)];
v324533 = rgs_transform(vector(1+up_to, n, Aux324533(n-1)));
A324533(n) = v324533[1+n];
CROSSREFS
Cf. also A323889 (compare the scatterplots).
Sequence in context: A366880 A324345 A368695 * A141128 A160180 A319351
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 05 2019
STATUS
approved