cp's OEIS Frontend

A277312 Smallest k such that k - lambda(k) = prime(n), where lambda(k) = A002322(k).

%I A277312 #21 Nov 08 2016 22:20:25
%S A277312 4,9,25,49,15,169,289,361,33,841,961,1369,1681,1849,69,65,87,3721,
%T A277312 4489,115,5329,91,123,7921,9409,10201,10609,159,11881,12769,16129,215,
%U A277312 18769,19321,185,22801,24649,26569,249,221,267,32761,329,37249,38809,39601,247,259,339,52441
%N A277312 Smallest k such that k - lambda(k) = prime(n), where lambda(k) = A002322(k).
%C A277312 a(n) is the smallest k such that A277127(k) = A000040(n).
%C A277312 a(n) <= prime(n)^2, because p^2 - lambda(p^2) = p prime.
%C A277312 Conjecture: a(n) = prime(n)^2 for infinitely many n.
%C A277312 For n > 1, a(n) is an odd composite. - _Robert Israel_, Oct 14 2016
%H A277312 Robert Israel, <a href="/A277312/b277312.txt">Table of n, a(n) for n = 1..446</a>
%p A277312 N:= 100: # to get a(1)..a(N)
%p A277312 A:= Vector(N):
%p A277312 A[1]:= 4:
%p A277312 count:= 1:
%p A277312 for k from 9 by 2 while count < N do
%p A277312   r:= k - numtheory:-lambda(k);
%p A277312   if isprime(r) then
%p A277312     n:= numtheory:-pi(r);
%p A277312     if n <= N and A[n] = 0 then
%p A277312       count:= count+1;
%p A277312       A[n]:= k;
%p A277312     fi
%p A277312    fi
%p A277312 od:
%p A277312 convert(A,list); # _Robert Israel_, Oct 14 2016
%t A277312 Table[k = 1; While[k - CarmichaelLambda@ k != Prime@ n, k++]; k, {n, 50}] (* _Michael De Vlieger_, Oct 14 2016 *)
%o A277312 (PARI) a(n) = {my(k = 1); while (k - lcm(znstar(k)[2]) != prime(n), k++); k;} \\ _Michel Marcus_, Oct 09 2016
%Y A277312 Cf. A000040, A002322, A053194, A277127, A278021.
%K A277312 nonn
%O A277312 1,1
%A A277312 _Thomas Ordowski_, Oct 09 2016
%E A277312 More terms from _Altug Alkan_, Oct 09 2016