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A277312 Smallest k such that k - lambda(k) = prime(n), where lambda(k) = A002322(k). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A082200 A244557 A063482 * A069557 A230312 A332646

Adjacent sequences:  A277309 A277310 A277311 * A277313 A277314 A277315

KEYWORD

nonn

AUTHOR

Thomas Ordowski, Oct 09 2016

EXTENSIONS

More terms from Altug Alkan, Oct 09 2016

STATUS

approved

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Last modified August 5 21:58 EDT 2020. Contains 336213 sequences. (Running on oeis4.)