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A122258 Number of Pierpont primes <= n.

%I A122258 #10 May 14 2025 04:27:41
%S A122258 0,1,2,2,3,3,4,4,4,4,4,4,5,5,5,5,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
%T A122258 7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%U A122258 8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10
%N A122258 Number of Pierpont primes <= n.
%H A122258 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a>.
%F A122258 a(n) <= A000720(n).
%F A122258 a(n) <= A071521(n).
%t A122258 smooth3Q[n_] := Times @@ ({2, 3}^IntegerExponent[n, {2, 3}]) == n; s[n_] := Boole[PrimeQ[n] && smooth3Q[n-1]]; Accumulate[Table[s[n], {n, 1, 100}]] (* _Amiram Eldar_, May 14 2025 *)
%o A122258 (PARI) is3smooth(n) = my(m = n >> valuation(n, 2)); m == 3^valuation(m, 3);
%o A122258 f(n) = isprime(n) && is3smooth(n-1);
%o A122258 list(lim) = {my(s = 0); for(n = 1, lim, s += f(n); print1(s, ", "));} \\ _Amiram Eldar_, May 14 2025
%Y A122258 Partial sums of A122257.
%Y A122258 Cf. A000720, A005109, A071521.
%K A122258 nonn
%O A122258 1,3
%A A122258 _Reinhard Zumkeller_, Aug 29 2006