Search: id:A014092
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%I A014092
%S A014092 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,
%T A014092 95,97,101,107,113,117,119,121,123,125,127,131,135,137,143,145,147,149,
%U A014092 155,157,161,163,167,171,173,177,179,185,187,189,191,197,203,205,207,209
%N A014092 Numbers that are not the sum of 2 primes.
%C A014092 Suggested by the Goldbach conjecture that every even number is the sum 
               of 2 primes.
%C A014092 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.
%C A014092 Values of n such that A061358(n)=0. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 03 2006
%C A014092 Values of n such that A073610(n)=0 - Graeme McRae (g_m(AT)mcraefamily.com), 
               Jul 18 2006
%D A014092 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).
%H A014092 <a href="Sindx_Go.html#Goldbach">Index entries for sequences related 
               to Goldbach conjecture</a>
%F A014092 Odd composite numbers + 2 (essentially A014076(n) + 2 ).
%p A014092 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 (deutsch(AT)duke.poly.edu), Apr 03 2006
%t A014092 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 (MTaktikos(AT)alice-dsl.net), Dec 
               30 2007
%o A014092 (PARI) isA014092(n)={ local p ; i=1 ; p=prime(i) ; while(p<n, if( isprime(n-p), 
               return(0) ; ) ; i++ ; p=prime(i) ; ) ; return(1) ; } { n=1 ; for(a=1,
               200, if(isA014092(a), print(n," ",a) ; n++ ; ) ; ) ; } - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Aug 20 2006
%Y A014092 Cf. A002372, A002373, A002374, A048974.
%Y A014092 Cf. A061358.
%Y A014092 Sequence in context: A051080 A051098 A051076 this_sequence A100962 A045337 
               A098700
%Y A014092 Adjacent sequences: A014089 A014090 A014091 this_sequence A014093 A014094 
               A014095
%K A014092 nonn,nice,easy
%O A014092 1,2
%A A014092 N. J. A. Sloane (njas(AT)research.att.com).

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