A374577 - OEIS

%I #34 Sep 02 2024 08:40:03

%S 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 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 22,11,21,1,13,12,11,26,25,30,19,24,20,27,16,23,11

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

%C This sequence gives the exponents of 2's in the Pierpont primes, A374578 gives the exponents of 3's.

%H Amiram Eldar, <a href="/A374577/b374577.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007814(A005109(n)-1).

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

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

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

%t 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 (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 Cf. A005109, A007814, A374578.

%K nonn

%O 1,3

%A _William C. Laursen_, Jul 11 2024

%E More terms from _Stefano Spezia_, Jul 12 2024