A251609 Least k such that prime(k) + prime(k+1) contains n distinct prime divisors.

1, 3, 6, 27, 276, 1755, 24865, 646029, 7946521, 195711271, 4129119136, 198635909763, 6351380968517, 322641218722443, 11068897188590241, 501741852481602261, 24367382928343066431, 1292304206793356882286

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = A000720(A230518(n)). - Amiram Eldar, Feb 17 2019

Example

a(1) = 1 because prime(1) + prime(2) = 2 + 3 = 5, which is a prime power and so has one distinct prime divisor; the other prime indices yielding a prime power are 2, 18, 564,...(A071352) since prime(2) + prime(3) = 3 + 5 = 2^3, prime(18) + prime(19) = 61 + 67 = 2^7, prime(564) + prime(565)= 4093 + 4099 = 2^13,...

Maple

N:= 10^6: # to use primes <= N
Primes:= select(isprime, [2, seq(2*i+1, i=1..(N-1)/2)]):
for i from 1 to nops(Primes)-1 do
  f:= nops(numtheory:-factorset(Primes[i]+Primes[i+1]));
  if not assigned(A[f]) then A[f]:= i fi
od:
seq(A[j], j=1..max(indices(A))); # Robert Israel, Dec 05 2014

Mathematica

lst={}; Do[k=1; While[Length[FactorInteger[Prime[k]+Prime[k+1]]]!=n, k++]; AppendTo[lst, k], {n, 1, 5}]; lst

Crossrefs

Cf. A000040, A001221, A071352, A230518, A251600.

Sequence in context: A372039 A270889 A097678 * A366560 A074894 A324146

Adjacent sequences: A251606 A251607 A251608 * A251610 A251611 A251612

Keyword

nonn,more

Author

Michel Lagneau, Dec 05 2014

Extensions

a(10)-a(18) from Amiram Eldar, Feb 17 2019

Status

approved