A251600 Least k such that prime(k) + prime(k+1) contains n prime divisors (with multiplicity), otherwise 0.

1, 0, 2, 5, 16, 20, 18, 43, 162, 190, 532, 916, 564, 3314, 3908, 10499, 30789, 53828, 153384, 62946, 278737, 364195, 629686, 3768344, 7827416, 9496221, 23159959, 184328920, 68035462, 92566977, 457932094, 370110663, 648634305, 4032924162, 7841376455

Offset

1,3

Comments

If p and q are two consecutive odd primes, then p + q is the product of at least three primes (not necessarily distinct) because p + q = 2*(p + q)/2 => (p + q)/2 is a composite integer between two consecutive primes p and q that is the product of at least two prime numbers. Thus 2*(p + q)/2 has at least three prime factors => a(1) = 1 because prime(1) is even => prime(1) + prime(2) = 5 is prime and a(2) = 0, probably the only 0 of the sequence.

Links

Giovanni Resta, Table of n, a(n) for n = 1..45

Example

a(5) = 16 because prime(16) + prime(17) = 53 + 59 = 112 = 7*2^4 with 5 prime divisors.

Mathematica

A251600 = {1, 0}; Do[k = 1; While[PrimeOmega[Prime[k] + Prime[k + 1]] != n, k++]; AppendTo[A251600, k], {n, 3, 10}]; A251600

Crossrefs

Cf. A000040, A001222.

Sequence in context: A098048 A257348 A101847 * A117557 A175735 A275172

Adjacent sequences: A251597 A251598 A251599 * A251601 A251602 A251603

Keyword

nonn

Author

Michel Lagneau, Dec 05 2014

Extensions

a(28)-a(33) from Daniel Suteu, Nov 18 2018

a(34)-a(35) from Giovanni Resta, Nov 19 2018

Status

approved