A109314 Numbers n such that prime(n) + n is a prime power (A246547).

3, 5, 8, 9, 12, 86, 230, 503, 1170, 2660, 2772, 6288, 6572, 8858, 9590, 14870, 16332, 17708, 53132, 54540, 63890, 64908, 82830, 93068, 98132, 104726, 119298, 136502, 152198, 177918, 187040, 234650, 241682, 253118, 263930, 278970, 376680, 412440, 456110, 469034

Offset

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Formula

prime(n) + n = q^k, q is prime and k_Integer >= 2.

Example

2660 is OK because prime(2660) + 2660 = 23909 + 2660 = 26569 = 163^2, 163 is prime.

Maple

ispp:= n -> not isprime(n) and nops(numtheory:-factorset(n))=1:
p:= 1: Res:= NULL:
for n from 1 to 10^6 do
  p:= nextprime(p);
  if ispp(n+p) then Res:= Res, n fi
od:
Res; # Robert Israel, Jun 08 2016

Mathematica

lst = {}; fQ[n_] := Block[{pf = FactorInteger[n]}, (2-Length[pf])(pf[[1, 2]]-1) > 0]; Do[ If[ fQ[Prime[n] + n], Print[n]; AppendTo[lst, n]], {n, 456109}]; lst

Prog

(Sage) def np(n): return n+nth_prime(n)
[n for n in (1..10000) if not np(n).is_prime() and np(n).is_prime_power()] # Giuseppe Coppoletta, Jun 08 2016
(PARI) isok(n) = isprimepower(n+prime(n)) >= 2; \\ Michel Marcus, Jun 18 2017

Crossrefs

Cf. A025475 = powers of a prime but not prime, also nonprime n such that sigma(n)*phi(n) > (n-1)2; A107708 = values of q, A107709 = values of k; A107710 = values of prime (A109314(n)).

Cf. A107605, A246547.

Sequence in context: A051206 A081451 A107605 * A319828 A325540 A102529

Adjacent sequences: A109311 A109312 A109313 * A109315 A109316 A109317

Keyword

nonn

Author

Zak Seidov and Robert G. Wilson v, Jun 25 2005

Status

approved