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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A038752 A125714 A247953 * A004038 A152038 A105614

Adjacent sequences:  A284088 A284089 A284090 * A284092 A284093 A284094

KEYWORD

nonn

AUTHOR

Zak Seidov, Mar 19 2017

STATUS

approved

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Last modified June 18 17:05 EDT 2019. Contains 324214 sequences. (Running on oeis4.)