A086827 - OEIS

%I #26 Oct 06 2023 10:41:16

%S 3,11,59,71,191,1151,14591,15359,138239,675839,737279,786431,22118399,

%T 36175871,63700991,138412031,169869311,1321205759,4076863487,

%U 10871635967,24159191039,370440929279,1793819934719,2348273369087,14637248544767,56358560858111,79164837199871,659706976665599

%N Smaller member of a twin prime pair such that the sum sets a record for number of prime divisors (counted with multiplicity).

%H David A. Corneth, <a href="/A086827/b086827.txt">Table of n, a(n) for n = 1..107</a>

%e 191:193 are twin primes and 384 has 8 prime divisors.

%e 1151:1153 are twin primes and 2304 has 10 prime divisors.

%o (PARI) g(n) = isprime(n/2 - 1) && isprime(n/2 + 1);

%o m = 0; forprime(n = 3, 10000, if (isprime(n + 2), c = bigomega(2*n + 2); if (c > m, m = c; print(n))));

%o while (m < 50, found = 0; for (i = m - 6, m, for (j = max(1, m - 1 - i), m + 4 - i, for (k = 2, 5, for (l = k, 15, n = 2^i*3^j*prime(k)*prime(l); if (g(n), if (!found || found > n, found = n)))))); t = log(found/2^m/3)/log(1.5); t = round(t); a = found/2^(m - t)/3; x = 0; i = 2^t; while (!x, if (bigomega(i) >= t, n = 2^(m - t)*3*i; if (g(n), x = n)); i++); m = bigomega(x); print(x/2 - 1)); \\ _David Wasserman_, Mar 30 2005

%Y Subsequence of A001359.

%Y Cf. A001222.

%K nonn

%O 1,1

%A _Jason Earls_, Aug 07 2003

%E More terms from _David Wasserman_, Mar 30 2005

%E Offset 1 from _Michel Marcus_, Sep 25 2023

%E More terms from _David A. Corneth_, Sep 26 2023