A319706 Filter sequence which for primes p records the prime signature of 2p+1, and for all other numbers assigns a unique number.

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

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; };
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- A046523, A305800, A305810, A305900, A305901, A305978, A305985.

Cf. A005384 (positions of 2's), A234095 (positions of 5's).

Sequence in context: A304105 A305978 A305985 * A305894 A305811 A239471

Adjacent sequences: A319703 A319704 A319705 * A319707 A319708 A319709

Keyword

nonn

Author

Antti Karttunen, Sep 26 2018

Status

approved