A352888 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278219(A109812(i)) = A278219(A109812(j)), for all i, j >= 1.

1, 2, 2, 1, 2, 3, 4, 2, 5, 6, 7, 5, 6, 5, 2, 1, 5, 6, 4, 3, 7, 6, 4, 8, 7, 6, 5, 1, 2, 9, 10, 7, 11, 12, 6, 9, 13, 7, 3, 5, 6, 7, 6, 5, 6, 9, 4, 6, 9, 2, 6, 12, 6, 5, 11, 7, 13, 14, 7, 15, 13, 12, 16, 9, 14, 11, 12, 5, 6, 7, 11, 12, 6, 5, 5, 1, 4, 13, 7, 8, 15, 16, 12, 11, 9, 10, 12, 11, 12, 10, 14, 17, 14, 16, 18

Offset: 1

Author

Antti Karttunen, Apr 07 2022

Keywords

• nonn
• base
• look

Comments

Restricted growth sequence transform of A278219(A109812(n)).

For all i, j: a(i) = a(j) => A352889(i) = A352889(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A109812, A278219, A352889.

Cf. also A286619, A351578, A351963.

Programs

PARI

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; };
v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '
up_to = #v109812;
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);
A278219(n) = A046523(A005940(1+A003188(n)));
A109812(n) = v109812[n];
v352888 = rgs_transform(vector(up_to, n, A278219(A109812(n))));
A352888(n) = v352888[n];