

A251600


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


3



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
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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



