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

1,1

Links

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

Formula

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

Example

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.

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}]&]

Prog

(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

Crossrefs

A241945 is a subsequence.

Cf. A000040, A001222.

Sequence in context: A125714 A361593 A247953 * A004038 A152038 A105614

Adjacent sequences: A284088 A284089 A284090 * A284092 A284093 A284094

Keyword

nonn

Author

Zak Seidov, Mar 19 2017

Status

approved