A324401 - OEIS

A324401

Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = -1 if n is an odd prime, f(n) = -2 if n = 2^k, with k > 1, and f(n) = n for all other numbers.

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

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OFFSET

1,2

COMMENTS

For all i, j:

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

a(i) = a(j) => A305976(i) = A305976(j) => A001221(i) = A001221(j),

a(i) = a(j) => A322591(i) = A322591(j),

a(i) = a(j) => A323235(i) = A323235(j),

a(i) = a(j) => A324399(i) = A324399(j),

a(i) = a(j) => A297159(i) = A297159(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

If n <= 2, a(n) = n, for n > 2, if n is an odd prime, a(n) = 3, if n = 2^k, with k >= 2, a(n) = 4, otherwise a(n) = 4 + n - A000523(n) - A000720(n).

PROG

(PARI)

A000523(n) = if(n<1, 0, #binary(n)-1);

A324401(n) = if(n<4, n, if(isprime(n), 3, if(!bitand(n, n-1), 4, 4+n-A000523(n)-primepi(n))));

(PARI)

up_to = 65537;

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; };

Aux324401(n) = if((n>2) && (isprime(n)||!bitand(n, n-1)), -(2-(n%2)), n);

\\ Equally: Aux324401(n) = if(n<=2, n, if(isprime(n), -1, if(!bitand(n, n-1), -2, n)));

v324401 = rgs_transform(vector(up_to, n, Aux324401(n)));

A324401(n) = v324401[n];

CROSSREFS

Cf. A000523, A000720.

Cf. also A297159, A305801, A305976, A322591, A323235, A324399, A324400.

Sequence in context: A322814 A324399 A325382 * A323082 A212356 A322816

Adjacent sequences: A324398 A324399 A324400 * A324402 A324403 A324404

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 01 2019

STATUS

approved