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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
Jonathan Bayless, Dominic Klyve, and Tomás Oliveira e Silva, New Bounds and Computations on Prime-Indexed Primes, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A43, 2013.
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
Equals 2*A174682. - Michel Marcus, May 18 2018
Sequence in context: A349080 A337837 A064361 * A064407 A309519 A198392
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 13 2018
STATUS
approved

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Last modified March 19 07:25 EDT 2024. Contains 370955 sequences. (Running on oeis4.)