VOOZH about

URL: https://oeis.org/A319706

⇱ A319706 - OEIS

login
A319706
Filter sequence which for primes p records the prime signature of 2p+1, and for all other numbers assigns a unique number.
4
1, 2, 2, 3, 2, 4, 5, 6, 7, 8, 2, 9, 10, 11, 12, 13, 5, 14, 5, 15, 16, 17, 2, 18, 19, 20, 21, 22, 2, 23, 24, 25, 26, 27, 28, 29, 24, 30, 31, 32, 2, 33, 5, 34, 35, 36, 5, 37, 38, 39, 40, 41, 2, 42, 43, 44, 45, 46, 5, 47, 5, 48, 49, 50, 51, 52, 53, 54, 55, 56, 5, 57, 24, 58, 59, 60, 61, 62, 5, 63, 64, 65, 2, 66, 67, 68, 69, 70, 2, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 5
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of function f defined as f(n) = A046523(2n+1) when n is a prime, otherwise -n.
For all i, j:
A305810(i) = A305810(j) => a(i) = a(j),
and
a(i) = a(j) => A305800(i) = A305800(j),
a(i) = a(j) => A305978(i) = A305978(j),
a(i) = a(j) => A305985(i) = A305985(j).
LINKS
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A319706aux(n) = if(isprime(n), A046523(n+n+1), -n);
v319706 = rgs_transform(vector(up_to, n, A319706aux(n)));
A319706(n) = v319706[n];
CROSSREFS
Cf. A005384 (positions of 2's), A234095 (positions of 5's).
Sequence in context: A304105 A305978 A305985 * A305894 A305811 A239471
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 26 2018
STATUS
approved