A366877 Lexicographically earliest infinite sequence such that a(i) = a(j) => A337377(i) = A337377(j) for all i, j >= 0, where A337377 is the primorial deflation (denominator) of Doudna sequence.

1, 1, 2, 1, 3, 1, 4, 1, 5, 3, 2, 1, 6, 2, 7, 1, 8, 5, 9, 3, 3, 1, 4, 1, 10, 6, 11, 1, 12, 4, 13, 1, 14, 8, 15, 5, 16, 5, 17, 3, 5, 3, 2, 1, 6, 2, 7, 1, 18, 10, 19, 6, 20, 3, 4, 1, 21, 12, 22, 2, 23, 7, 24, 1, 25, 14, 26, 8, 27, 8, 28, 5, 29, 16, 15, 5, 30, 9, 31, 3, 8, 5, 9, 3, 3, 1, 4, 1, 10, 6, 11, 1, 12, 4, 13, 1, 32, 18

Offset: 0

Author

Antti Karttunen, Oct 26 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of A337377.

Links

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

Crossrefs

Cf. A005940, A064989, A319627, A337377.

Cf. also A366876.

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A319627(n) = (A064989(n) / gcd(n, A064989(n)));
A337377(n) = A319627(A005940(1+n));
v366877 = rgs_transform(vector(1+up_to,n,A337377(n-1)));
A366877(n) = v366877[1+n];