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Numbers n such that prime(n+1)-prime(n) = tau(n) = A000005(n).
4

%I #15 Aug 22 2016 11:59:48

%S 1,2,3,5,6,7,8,13,14,17,18,22,24,27,32,38,41,43,65,76,80,83,85,89,93,

%T 95,109,113,122,128,134,135,143,155,159,164,173,180,183,186,188,213,

%U 226,235,237,243,245,246,247,248,249,254,275,277,284,287,292,301,303

%N Numbers n such that prime(n+1)-prime(n) = tau(n) = A000005(n).

%H R. J. Mathar, <a href="/A068526/b068526.txt">Table of n, a(n) for n = 1..10159</a>

%e 1 has 1 divisor, prime(1) is 2, and 2+1=3 is prime(1+1), so 1 is in the sequence.

%e 2 has 2 divisors, prime(2) is 3, and 3+2=5 is prime(2+1), so 2 is in the sequence.

%p with(numtheory): A068526:=n->`if`(ithprime(n+1)-ithprime(n)=tau(n), n, NULL): seq(A068526(n), n=1..500); # _Wesley Ivan Hurt_, Apr 10 2015

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Mar 21 2002