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
Keywords
Examples
2660 is OK because prime(2660) + 2660 = 23909 + 2660 = 26569 = 163^2, 163 is prime.
Links
- Donovan Johnson, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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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
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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 -
PARI
isok(n) = isprimepower(n+prime(n)) >= 2; \\ Michel Marcus, Jun 18 2017
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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
Formula
prime(n) + n = q^k, q is prime and k_Integer >= 2.