A319704 Filter sequence which records for primes their residue modulo 4, and for all other numbers assigns a unique number.

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

Offset

1,2

Comments

Restricted growth sequence transform of function f defined as f(n) = A010873(n) when n is a prime, otherwise -n.

For all i, j:

a(i) = a(j) => A010873(i) = A010873(j),

a(i) = a(j) => A305801(i) = A305801(j),

a(i) = a(j) => A319714(i) = A319714(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; };
A319704aux(n) = if(isprime(n), -(n%4), n);
v319704 = rgs_transform(vector(up_to, n, A319704aux(n)));
A319704(n) = v319704[n];

Crossrefs

Cf. A010873, A305801, A319714.

Cf. A002145 (positions of 3's), A002144 (positions of 5's).

Cf. also A319350, A319705, A319706.

Sequence in context: A319994 A319714 A320004 * A331304 A343721 A070675

Adjacent sequences: A319701 A319702 A319703 * A319705 A319706 A319707

Keyword

nonn

Author

Antti Karttunen, Sep 26 2018

Status

approved