|
%I #15 Oct 16 2021 13:06:04
%S 0,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%N Characteristic function of Pierpont primes (A005109).
%H Antti Karttunen, <a href="/A122257/b122257.txt">Table of n, a(n) for n = 1..65537</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = A010051(n) * A065333(n-1).
%F a(n) = if (n is prime) and (n-1 is 3-smooth) then 1 else 0.
%F a(n) = if n=1 then 0 else A122258(n) - A122258(n-1);
%F a(A122259(n)) = 0, a(A005109(n)) = 1.
%t smooth3Q[n_] := n == 2^IntegerExponent[n, 2]*3^IntegerExponent[n, 3];
%t a[n_] := Boole[PrimeQ[n] && smooth3Q[n - 1]];
%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Oct 16 2021 *)
%o (Scheme)
%o (define (A122257 n) (if (= 1 n) 0 (if (= 1 (A065333 (- n 1))) (A010051 n) 0)))
%o (define (A065333 n) (if (= 1 (A038502 (A000265 n))) 1 0))
%o ;; _Antti Karttunen_, Dec 07 2017
%Y Cf. A005109, A010051, A065333, A122258 (partial sums).
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Aug 29 2006
|
