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

1,2

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

Prog

(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];

Crossrefs

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

Cf. also A319704, A319706.

Sequence in context: A278064 A333358 A305795 * A331746 A327886 A331166

Adjacent sequences: A319702 A319703 A319704 * A319706 A319707 A319708

Keyword

nonn

Author

Antti Karttunen, Sep 26 2018

Status

approved