A277312 - OEIS

%I #21 Nov 08 2016 22:20:25

%S 4,9,25,49,15,169,289,361,33,841,961,1369,1681,1849,69,65,87,3721,

%T 4489,115,5329,91,123,7921,9409,10201,10609,159,11881,12769,16129,215,

%U 18769,19321,185,22801,24649,26569,249,221,267,32761,329,37249,38809,39601,247,259,339,52441

%N Smallest k such that k - lambda(k) = prime(n), where lambda(k) = A002322(k).

%C a(n) is the smallest k such that A277127(k) = A000040(n).

%C a(n) <= prime(n)^2, because p^2 - lambda(p^2) = p prime.

%C Conjecture: a(n) = prime(n)^2 for infinitely many n.

%C For n > 1, a(n) is an odd composite. - _Robert Israel_, Oct 14 2016

%H Robert Israel, <a href="/A277312/b277312.txt">Table of n, a(n) for n = 1..446</a>

%p N:= 100: # to get a(1)..a(N)

%p A:= Vector(N):

%p A[1]:= 4:

%p count:= 1:

%p for k from 9 by 2 while count < N do

%p   r:= k - numtheory:-lambda(k);

%p   if isprime(r) then

%p     n:= numtheory:-pi(r);

%p     if n <= N and A[n] = 0 then

%p       count:= count+1;

%p       A[n]:= k;

%p     fi

%p    fi

%p od:

%p convert(A,list); # _Robert Israel_, Oct 14 2016

%t Table[k = 1; While[k - CarmichaelLambda@ k != Prime@ n, k++]; k, {n, 50}] (* _Michael De Vlieger_, Oct 14 2016 *)

%o (PARI) a(n) = {my(k = 1); while (k - lcm(znstar(k)[2]) != prime(n), k++); k;} \\ _Michel Marcus_, Oct 09 2016

%Y Cf. A000040, A002322, A053194, A277127, A278021.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Oct 09 2016

%E More terms from _Altug Alkan_, Oct 09 2016