A336855 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), for all i, j >= 1, where f(p) = p-nextprime(p) for primes p, and f(n) = n for all other numbers.

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

Offset

1,2

Comments

Restricted growth sequence transform of function f defined as: f(n) = -{distance to the next larger prime} when n is a prime, otherwise f(n) = -n.

For all i, j:

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

a(i) = a(j) => A336852(i) = A336852(j),

a(i) = a(j) => A336853(i) = A336853(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for primes, gaps between

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; };
A336855aux(n) = if(isprime(n), n-nextprime(1+n), n);
v336855 = rgs_transform(vector(up_to, n, A336855aux(n)));
A336855(n) = v336855[n];

Crossrefs

Cf. also A001359 (positions of 3's), A305801, A319704, A331304, A336852, A336853.

Sequence in context: A332826 A353840 A319350 * A329895 A342552 A078908

Adjacent sequences: A336852 A336853 A336854 * A336856 A336857 A336858

Keyword

nonn

Author

Antti Karttunen, Aug 09 2020

Status

approved