|
|
A303403
|
|
Even numbers that are not the sum of two prime-indexed primes.
|
|
2
|
|
|
2, 4, 12, 18, 24, 26, 30, 32, 38, 40, 50, 54, 56, 60, 66, 68, 74, 80, 92, 96, 102, 104, 106, 110, 116, 122, 128, 136, 146, 148, 152, 154, 156, 164, 170, 172, 178, 180, 200, 204, 206, 212, 226, 230, 234, 248, 256, 260, 264, 268, 276, 290, 292, 296, 298, 302
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Bayless et al. conjectured that every even number larger than 80612 is the sum of two prime-indexed primes. If the conjecture is true then this sequence is finite with 733 terms.
Similarly, it appears that 322704332 is the largest of the 1578727 even numbers that cannot be written as prime(prime(prime(i))) + prime(prime(prime(j)). - Giovanni Resta, May 31 2018
|
|
LINKS
|
|
|
EXAMPLE
|
20 is not in the sequence since 20 = 17 + 3 = prime(7) + prime(2). 2 and 7 are primes, so 3 and 17 are prime-indexed primes. - Michael B. Porter, May 21 2018
|
|
MATHEMATICA
|
pipQ[n_]:=PrimeQ[n]&&PrimeQ[PrimePi[n]]; s1falsifiziertQ[s_]:= Module[{ip=IntegerPartitions[s, {2}], widerlegt=False}, Do[If[pipQ[ip[[i, 1]] ] ~And~ pipQ [ip[[i, 2]] ], widerlegt = True; Break[]], {i, 1, Length[ip]}]; widerlegt]; Select[Range[2500], EvenQ[#]&& s1falsifiziertQ[ # ]==False&] (* after Michael Taktikos at A014092 *)
(* or *) p = Prime@ Prime@ Range@ PrimePi@ PrimePi@ 302; Select[Range[2, 302, 2], IntegerPartitions[#, {2}, p] == {} &] (* Giovanni Resta, May 31 2018 *)
|
|
PROG
|
(PARI) isok(n) = {if (n % 2, return (0)); forprime(p=2, n/2, if (isprime(primepi(p)) && isprime(n-p) && isprime(primepi(n-p)), return (0)); ); return (1); } \\ Michel Marcus, May 18 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|