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 A014092 Numbers that are not the sum of 2 primes. 47
 1, 2, 3, 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, 97, 101, 107, 113, 117, 119, 121, 123, 125, 127, 131, 135, 137, 143, 145, 147, 149, 155, 157, 161, 163, 167, 171, 173, 177, 179, 185, 187, 189, 191, 197, 203, 205, 207, 209 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Suggested by the Goldbach conjecture that every even number larger than 2 is the sum of 2 primes. Since (if we believe the Goldbach conjecture) all the entries > 2 in this sequence are odd, they are equal to 2 + an odd composite number (or 1). Otherwise said, the sequence consists of 2 and odd numbers k such that k-2 is not prime. In particular there is no element from A006512, greater of a twin prime pair. - M. F. Hasler, Sep 18 2012 Values of k such that A061358(k) = 0. - Emeric Deutsch, Apr 03 2006 Values of k such that A073610(k) = 0. - Graeme McRae, Jul 18 2006 REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Section 2.8 (for Goldbach conjecture). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Odd composite numbers + 2 (essentially A014076(n) + 2 ). Equals {2} union A005408 \ A052147, i.e., essentially the complement of A052147 (or rather A048974) within the odd numbers A005408. - M. F. Hasler, Sep 18 2012 MAPLE g:=sum(sum(x^(ithprime(i)+ithprime(j)), i=1..j), j=1..50): gser:=series(g, x=0, 230): a:=proc(n) if coeff(gser, x^n)=0 then n else fi end: seq(a(n), n=1..225); # Emeric Deutsch, Apr 03 2006 MATHEMATICA s1falsifiziertQ[s_]:= Module[{ip=IntegerPartitions[s, {2}], widerlegt=False}, Do[If[PrimeQ[ip[[i, 1]] ] ~And~ PrimeQ[ip[[i, 2]] ], widerlegt = True; Break[]], {i, 1, Length[ip]}]; widerlegt]; Select[Range[250], s1falsifiziertQ[ # ]==False&] (* Michael Taktikos, Dec 30 2007 *) Join[{1, 2}, Select[Range[3, 300, 2], !PrimeQ[#-2]&]] (* Zak Seidov, Nov 27 2010 *) Select[Range[250], Count[IntegerPartitions[#, {2}], _?(AllTrue[#, PrimeQ]&)]==0&] (* Harvey P. Dale, Jun 08 2022 *) PROG (PARI) isA014092(n)=local(p, i) ; i=1 ; p=prime(i); while(p all ((== 0) . a010051) \$ map (x -) \$ takeWhile (< x) a000040_list) [1..] -- Reinhard Zumkeller, Sep 28 2011 (Python) from sympy import prime, isprime def ok(n): i=1 x=prime(i) while x

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Last modified November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)