A323074 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = -(n mod 4) if n is a prime, and f(n) = A300840(n) for any other number.

1, 2, 3, 4, 5, 6, 3, 4, 7, 8, 3, 9, 5, 10, 11, 12, 5, 7, 3, 13, 14, 15, 3, 9, 16, 17, 18, 19, 5, 11, 3, 12, 20, 21, 22, 23, 5, 24, 25, 13, 5, 14, 3, 26, 27, 28, 3, 29, 30, 16, 31, 32, 5, 18, 33, 19, 34, 35, 3, 36, 5, 37, 38, 39, 40, 20, 3, 41, 42, 22, 3, 23, 5, 43, 44, 45, 46, 25, 3, 47, 48, 49, 3, 50, 51, 52, 53, 26, 5, 27, 54, 55, 56, 57, 58, 29, 5, 30, 59, 60, 5, 31, 3, 32

Offset

1,2

Comments

For all i, j:

A319704(i) = A319704(j) => a(i) = a(j) => A323082(i) = A323082(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65539

Prog

(PARI)
up_to = 65539;
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; };
ispow2(n) = (n && !bitand(n, n-1));
A302777(n) = ispow2(isprimepower(n));
A050376list(up_to) = { my(v=vector(up_to), i=0); for(n=1, oo, if(A302777(n), i++; v[i] = n); if(i == up_to, return(v))); };
v050376 = A050376list(up_to);
A050376(n) = v050376[n];
A052330(n) = { my(p=1, i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A052331(n) = { my(s=0, e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&A302777(n/d), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
A300840(n) = A052330(A052331(n)>>1);
A323074aux(n) = if(isprime(n), -(n%4), A300840(n));
v323074 = rgs_transform(vector(up_to, n, A323074aux(n)));
A323074(n) = v323074[n];

Crossrefs

Cf. A052330, A300840, A319704, A323081, A323082.

Sequence in context: A104148 A286450 A245344 * A195153 A328764 A323081

Adjacent sequences: A323071 A323072 A323073 * A323075 A323076 A323077

Keyword

nonn

Author

Antti Karttunen, Jan 04 2019

Status

approved