A145338 - OEIS

%I #15 May 05 2019 04:01:47

%S 7,2,11,197,23,37,47,401,59,1601,181,16901,167,3137,179,577,419,1297,

%T 1051,12101,359,739601,1009,4357,1511,50177,719,171610001,839,67601,

%U 10657,9096257,1439,240101,3697,145540097,3023,15877,2879,3587237,2521

%N a(n) is the smallest prime p where |d(p-1) - d(p+1)| = n. (d(m) = the number of divisors of m.)

%C a(2n-1) = k^2 + 1, for all positive integers n, where k is some integer; k is even for n >= 2.

%e a(2)=11 because abs(d(10) - d(12)) = 2 while abs(d(p-1) - d(p+1)) < 2 for p=2,3,5 and 7. - _Emeric Deutsch_, Oct 11 2008

%p with(numtheory); a:=proc(n) local j: for j while abs(tau(ithprime(j)-1)-tau(ithprime(j)+1)) <> n do end do: ithprime(j) end proc: seq(a(n), n=0..26); # _Emeric Deutsch_, Oct 11 2008

%Y Cf. A145337.

%K nonn

%O 0,1

%A _Leroy Quet_, Oct 08 2008

%E More terms from _R. J. Mathar_ and _Emeric Deutsch_, Oct 10 2008

%E Extended from a(27) onwards by _Ray Chandler_, Oct 12 2008