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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)