A124270 - OEIS

%I #16 Sep 17 2024 20:42:54

%S 7,19,34,41,53,44,38,103,91,73,99,75,135,142,147,118,133,125,118,193,

%T 229,191,212,202,197,201,216,213,248,239,209,248,279,279,277,277,333,

%U 325,350,327,299,308,264,309,314,322,297,281,363,374,461,488,484,482

%N a(n) = prime(A014612(n)) - A014612(prime(n)). Commutator [A000040,A014612] at n.

%H Giovanni Resta, <a href="/A124270/b124270.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000040(A014612(n)) - A014612(A000040(n)).

%F a(n) = A124268(n) - A124269(n).

%e a(1) = prime(3almostprime(1)) - 3almostprime(prime(1)) = prime(8) - 3almostprime(2) = 19 - 12 = 7.

%e a(2) = prime(3almostprime(2)) - 3almostprime(prime(2)) = prime(12) - 3almostprime(3) = 37 - 18 = 19.

%e a(3) = prime(3almostprime(3)) - 3almostprime(prime(3)) = prime(18) - 3almostprime(5) = 61 - 27 = 34.

%o (PARI) lista(nn) = {p = primes(nn); pp = select(x->bigomega(x)==3, vector(nn, n, n)); for (n=1, nn, print1(p[pp[n]] - pp[p[n]], ", "););} \\ _Michel Marcus_, Oct 15 2014

%Y Cf. A000040 (primes), A014612 (3-almost primes).

%Y Cf. A124268 (prime(3-almost prime(n))), A124269 (3-almost prime(prime(n))).

%Y Cf. A106349 (prime(semiprime(n))), A106350 (semiprime(prime(n))), A122824 (prime(semiprime(n)) - semiprime(prime(n))).

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Oct 23 2006