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Search: id:A157931
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| A157931 |
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Numbers that are both the sum and the product of two primes. |
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4
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| 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 38, 39, 46, 49, 55, 58, 62, 69, 74, 82, 85, 86, 91, 94, 106, 111, 115, 118, 122, 129, 133, 134, 141, 142, 146, 158, 159, 166, 169, 178, 183, 194, 201, 202, 206, 213, 214, 218, 226, 235, 253, 254, 259, 262, 265, 274, 278
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Assuming the Goldbach conjecture, this is A001358 intersect (A005843 union A052147), since an odd number n is the sum of two primes iff n-2 is prime. - N. J. A. Sloane, Mar 14 2009
The first few terms of A001358: Semiprimes, not members of A157931 are: 35, 51, 57, 65, 77, 87, 93, 95, ..., . [From Robert G. Wilson, v (rgwv(AT)rgwv.com), Mar 15 2009]
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LINKS
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Robert G. Wilson, v, Table of n, a(n) for n=1..1096.
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FORMULA
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A014091 INTERSECT A001358. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 15 2009]
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EXAMPLE
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For the numbers up to 100, the solutions are: 4 = (2+2) = (2*2); 6 = (3+3) = (2*3); 9 = (2+7) = (3*3); 10 = (3+7) = (2*5); 14 = (3+11) = (2*7); 15 = (2+13) = (3*5); 21 = (2+19) = (3*7); 22 = (3+19) = (2*11); 25 = (2+23) = (5*5); 26 = (3+23) = (2*13); 33 = (2+31) = (3*11); 34 = (3+31) = (2*17); 38 = (7+31) = (2*19); 39 = (2+37) = (3*13); 46 = (3+43) = (2*23); 49 = (2+47) = (7*7); 55 = (2+53) = (5*11); 58 = (5+53) = (2*29); 62 = (3+59) = (2*31); 69 = (2+67) = (3*23); 74 = (3+71) = (2*37); 82 = (3+79) = (2*41); 85 = (2+83) = (5*17); 86 = (3+83) = (2*43); 91 = (2+89) = (7*13); 94 = (5+89) = (2*47).
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MAPLE
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isA014091 := proc(n) for i from 1 do p := ithprime(i) ; if p > n/2 then RETURN(false); fi; if isprime(n-p) then RETURN(true) ; fi; od: end: isA001358 := proc(n) RETURN(numtheory[bigomega](n) = 2) ; end: for n from 4 to 500 do if isA001358(n) and isA014091(n) then printf("%d, ", n) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 15 2009]
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MATHEMATICA
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fQ[n_] := Block[{k = 2}, While[k < n, If[ PrimeQ[n - k], Break[]]; k = NextPrime@k]; k + 1 < n]; semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@n == 2; Select[ Range@ 295, fQ@# && semiPrimeQ@# &] [From Robert G. Wilson, v (rgwv(AT)rgwv.com), Mar 15 2009]
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CROSSREFS
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Cf. A001358, A005843, A052147, A062721.
Cf. A043326 Numbers n such that n is a product of two different primes and n-2 is prime, A062721 Numbers n such that n is a product of two primes and n-2 is prime. [From Zak Seidov (zakseidov(AT)yahoo.com), Mar 15 2009]
Sequence in context: A129336 A103607 A108574 this_sequence A046368 A113433 A115654
Adjacent sequences: A157928 A157929 A157930 this_sequence A157932 A157933 A157934
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KEYWORD
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easy,nonn,nice
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AUTHOR
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William Weeks (dach(AT)kuci.org), Mar 09 2009
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EXTENSIONS
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Edited by N. J. A. Sloane, Mar 14 2009
Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Robert G. Wilson, v (rgwv(AT)rgwv.com), Mar 15 2009
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