A284091 Indices n where prime(n) + 2*prime(n+1) and 2*prime(n) + prime(n+1) have the same number of prime divisors counted with multiplicity.

2, 3, 6, 11, 12, 15, 16, 17, 19, 20, 23, 25, 27, 30, 33, 34, 37, 38, 47, 48, 51, 53, 56, 57, 58, 60, 66, 68, 75, 76, 77, 78, 79, 86, 87, 89, 90, 93, 94, 99, 100, 101, 107, 110, 123, 124, 128, 133, 137, 138, 139, 141, 143, 145, 147, 151

Offset: 1

Author

Zak Seidov, Mar 19 2017

Keywords

• nonn

Examples

			n = 15, prime(n) = 47, prime(n+1) = 53, both 2*47 + 53 = 147 = 3*7^2 and 47 + 2*53 = 153 = 3^2*17 are products of 3 primes.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

A241945 is a subsequence.

Cf. A000040, A001222.

Programs

Maple

select(t -> numtheory:-bigomega(2*ithprime(t)+ithprime(t+1)) = numtheory:-bigomega(ithprime(t)+2*ithprime(t+1)), [$1..1000]); # Robert Israel, Mar 20 2017

Mathematica

Select[Range[1000],PrimeOmega[{2,1}.{(p=Prime[#]),(q=Prime[#+1])}]==PrimeOmega[{1,2}.{p,q}]&]

PARI

list(lim)=my(v=List(),p=2,n); forprime(q=3,, if(n++>lim, break); if(bigomega(p+2*q)==bigomega(2*p+q), listput(v,n)); p=q); Vec(v) \\ Charles R Greathouse IV, Mar 20 2017

Formula

n such that A001222(A000040(n)+2*A000040(n+1))=A001222(2*A000040(n)+A000040(n+1)). - Robert Israel, Mar 20 2017