%I #33 Sep 02 2024 08:40:06

%S 0,0,0,1,1,0,2,2,2,1,3,4,1,0,3,5,2,1,2,4,6,4,6,3,5,4,1,7,2,9,8,0,7,2,

%T 8,4,10,9,6,1,8,5,2,6,3,5,4,9,4,12,11,3,14,3,15,5,7,16,13,3,10,4,17,

%U 10,11,12,3,4,1,8,5,8,4,11,7,15,12,2,10,1,22,4

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

%C This sequence gives the exponents of 3's in the Pierpont primes, A374577 gives the exponents of 2's.

%H Amiram Eldar, <a href="/A374578/b374578.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007949(A005109(n)-1).

%e a(1) = 0, because the first Pierpont prime is 2 = 2^0 * 3^0 + 1.

%e a(6) = 0, because the sixth Pierpont prime is 17 = 2^4 * 3^0 + 1.

%e a(7) = 2, because the seventh Pierpont prime is 19 = 2^1 * 3^2 + 1.

%t With[{lim = 10^12}, IntegerExponent[Select[Sort@ Flatten@Table[2^i*3^j + 1, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}], PrimeQ] - 1, 3]] (* _Amiram Eldar_, Sep 02 2024 *)

%o (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, 3), ", ")));} \\ _Amiram Eldar_, Sep 02 2024

%Y Cf. A005109, A007949, A374577.

%K nonn

%O 1,7

%A _William C. Laursen_, Jul 11 2024

%E More terms from _Stefano Spezia_, Jul 12 2024