A086827 Smaller member of a twin prime pair such that the sum sets a record for number of prime divisors (counted with multiplicity).

3, 11, 59, 71, 191, 1151, 14591, 15359, 138239, 675839, 737279, 786431, 22118399, 36175871, 63700991, 138412031, 169869311, 1321205759, 4076863487, 10871635967, 24159191039, 370440929279, 1793819934719, 2348273369087, 14637248544767, 56358560858111, 79164837199871, 659706976665599

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..107

Example

191:193 are twin primes and 384 has 8 prime divisors.
1151:1153 are twin primes and 2304 has 10 prime divisors.

Prog

(PARI) g(n) = isprime(n/2 - 1) && isprime(n/2 + 1);
m = 0; forprime(n = 3, 10000, if (isprime(n + 2), c = bigomega(2*n + 2); if (c > m, m = c; print(n))));
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

Crossrefs

Subsequence of A001359.

Cf. A001222.

Sequence in context: A141776 A071698 A089188 * A308487 A164291 A137690

Adjacent sequences: A086824 A086825 A086826 * A086828 A086829 A086830

Keyword

nonn

Author

Jason Earls, Aug 07 2003

Extensions

More terms from David Wasserman, Mar 30 2005

Offset 1 from Michel Marcus, Sep 25 2023

More terms from David A. Corneth, Sep 26 2023

Status

approved