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A374577 Pierpont primes are primes of the form 2^t*3^u + 1; this sequence gives the t's in order.

%I A374577 #34 Sep 02 2024 08:40:03
%S A374577 0,1,2,1,2,4,1,2,3,5,2,1,6,8,4,1,6,8,7,4,1,5,2,7,4,7,12,3,11,1,3,16,6,
%T A374577 14,5,12,3,5,10,18,7,12,17,11,16,13,15,8,16,4,6,19,2,20,2,18,15,1,6,
%U A374577 22,11,21,1,13,12,11,26,25,30,19,24,20,27,16,23,11
%N A374577 Pierpont primes are primes of the form 2^t*3^u + 1; this sequence gives the t's in order.
%C A374577 This sequence gives the exponents of 2's in the Pierpont primes, A374578 gives the exponents of 3's.
%H A374577 Amiram Eldar, <a href="/A374577/b374577.txt">Table of n, a(n) for n = 1..10000</a>
%F A374577 a(n) = A007814(A005109(n)-1).
%e A374577 a(1) = 0, because the first Pierpont prime is 2 = 2^0 * 3^0 + 1.
%e A374577 a(6) = 4, because the sixth Pierpont prime is 17 = 2^4 * 3^0 + 1.
%e A374577 a(7) = 1, because the seventh Pierpont prime is 19 = 2^1 * 3^2 + 1.
%t A374577 With[{lim = 10^11}, IntegerExponent[Select[Sort@ Flatten@Table[2^i*3^j + 1, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}], PrimeQ] - 1, 2]] (* _Amiram Eldar_, Sep 02 2024 *)
%o A374577 (PARI) lista(lim) = {my(s = List()); for(i = 0, logint(lim, 2), for(j = 0, logint(lim >> i, 3), listput(s, 2^i * 3^j + 1))); s = Set(s); for(i = 1, #s, if(isprime(s[i]), print1(valuation(s[i] - 1, 2), ", ")));} \\ _Amiram Eldar_, Sep 02 2024
%Y A374577 Cf. A005109, A007814, A374578.
%K A374577 nonn
%O A374577 1,3
%A A374577 _William C. Laursen_, Jul 11 2024
%E A374577 More terms from _Stefano Spezia_, Jul 12 2024