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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A043272 A278064 A305795 * A304232 A303219 A071523

Adjacent sequences:  A319702 A319703 A319704 * A319706 A319707 A319708

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 26 2018

STATUS

approved

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Last modified September 18 18:38 EDT 2019. Contains 327180 sequences. (Running on oeis4.)