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Search: id:A014092
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| A014092 |
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Numbers that are not the sum of 2 primes. |
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+0
18
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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Suggested by the Goldbach conjecture that every even number 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.
Values of n such that A061358(n)=0. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 03 2006
Values of n such that A073610(n)=0 - Graeme McRae (g_m(AT)mcraefamily.com), Jul 18 2006
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REFERENCES
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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).
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LINKS
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Index entries for sequences related to Goldbach conjecture
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FORMULA
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Odd composite numbers + 2 (essentially A014076(n) + 2 ).
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MAPLE
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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
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MATHEMATICA
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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
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PROGRAM
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(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
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CROSSREFS
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Cf. A002372, A002373, A002374, A048974.
Cf. A061358.
Sequence in context: A051080 A051098 A051076 this_sequence A100962 A045337 A098700
Adjacent sequences: A014089 A014090 A014091 this_sequence A014093 A014094 A014095
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas
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