A319705 Filter sequence which for primes p records a distinct value for each distinct multiset formed from the lengths of 1-runs in its binary representation [A286622(p)], and for all other numbers assigns a unique number.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 13, 14, 15, 5, 16, 11, 17, 18, 19, 20, 21, 22, 23, 24, 25, 20, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 33, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 38, 48, 49, 50, 51, 52, 53, 54, 42, 55, 56, 57, 58, 59, 11, 60, 61, 62, 20, 63, 33, 64, 65, 66, 67, 68, 42, 69, 70, 71, 38, 72, 73, 74, 75, 76, 38, 77, 78, 79, 80, 81, 82, 83, 11, 84, 85, 86, 38

Offset: 1

Author

Antti Karttunen, Sep 26 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of function f defined as f(n) = A278222(n) when n is a prime, otherwise -n.

After its initial term 3, Fermat primes (A019434) gives the positions of 5 in this sequence, while the Mersenne primes (A000668) are each assigned to their own singleton equivalence class.

For all i, j:

a(i) = a(j) => A305900(i) = A305900(j),

a(i) = a(j) => A286622(i) = A286622(j),

a(i) = a(j) => A305795(i) = A305795(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A000668, A019434, A278222, A286163, A286622, A305795, A305900.

Cf. also A319704, A319706.

Programs

PARI

up_to = 100000;
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 };
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));
A319705aux(n) = if(isprime(n),A278222(n),-n);
v319705 = rgs_transform(vector(up_to,n,A319705aux(n)));
A319705(n) = v319705[n];