A340684 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A291759(n), A278222(A304759(n))], for all i, j >= 1.

1, 2, 1, 3, 4, 5, 6, 7, 8, 3, 9, 10, 1, 11, 12, 13, 14, 7, 4, 15, 14, 16, 9, 17, 18, 19, 20, 21, 22, 23, 24, 25, 9, 3, 8, 26, 24, 11, 27, 26, 28, 3, 29, 30, 22, 31, 1, 32, 33, 34, 35, 36, 14, 37, 35, 38, 39, 10, 40, 41, 22, 42, 43, 44, 45, 46, 4, 15, 47, 31, 40, 48, 49, 50, 51, 21, 52, 53, 54, 55, 56, 30, 24, 15

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A291759(n), A278222(A304759(n))].

For all i, j: a(i) = a(j) => A340383(i) = A340383(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Prog

(PARI)
up_to = 65537;
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291759(n) = A289814(A048673(n));
A289813(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A304759(n) = A289813(A048673(n));
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));
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; };
Aux340684(n) = [A291759(n), A278222(A304759(n))];
v340684 = rgs_transform(vector(up_to, n, Aux340684(n)));
A340684(n) = v340684[n];

Crossrefs

Cf. A048673, A278222, A290093, A291759, A304759, A340383.

Sequence in context: A304528 A360585 A175499 * A181440 A035043 A288118

Adjacent sequences: A340681 A340682 A340683 * A340685 A340686 A340687

Keyword

nonn

Author

Antti Karttunen, Jan 16 2021

Status

approved