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

4, 9, 25, 49, 15, 169, 289, 361, 33, 841, 961, 1369, 1681, 1849, 69, 65, 87, 3721, 4489, 115, 5329, 91, 123, 7921, 9409, 10201, 10609, 159, 11881, 12769, 16129, 215, 18769, 19321, 185, 22801, 24649, 26569, 249, 221, 267, 32761, 329, 37249, 38809, 39601, 247, 259, 339, 52441

Offset: 1

Author

Thomas Ordowski, Oct 09 2016

Keywords

• nonn

Comments

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

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

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

For n > 1, a(n) is an odd composite. - Robert Israel, Oct 14 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..446

Crossrefs

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

Programs

Maple

N:= 100: # to get a(1)..a(N)
A:= Vector(N):
A[1]:= 4:
count:= 1:
for k from 9 by 2 while count < N do
  r:= k - numtheory:-lambda(k);
  if isprime(r) then
    n:= numtheory:-pi(r);
    if n <= N and A[n] = 0 then
      count:= count+1;
      A[n]:= k;
    fi
   fi
od:
convert(A,list); # Robert Israel, Oct 14 2016

Mathematica

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

PARI

a(n) = {my(k = 1); while (k - lcm(znstar(k)[2]) != prime(n), k++); k;} \\ Michel Marcus, Oct 09 2016

Extensions

More terms from Altug Alkan, Oct 09 2016