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Search: id:A080435
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| A080435 |
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a(1) = 1; a(n) = least k > a(n-1) such that each prime of form a(i)+a(j) occurs for unique i <= j. |
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+0
4
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| 1, 2, 3, 5, 7, 8, 13, 14, 19, 20, 23, 25, 27, 31, 37, 43, 47, 49, 50, 55, 57, 61, 67, 73, 75, 79, 85, 91, 97, 98, 103, 107, 109, 111, 115, 121, 127, 131, 133, 135, 139, 140, 145, 151, 157, 163, 169, 175, 181, 185, 187, 193, 199, 200, 205, 211, 212, 217, 223, 229
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: There are infinitely many primes not of the form a(i)+a(j). - David W. Wilson (davidwwilson(AT)comcast.net), Apr 14 2003
Are there infinitely many even numbers in the sequence? - David W. Wilson (davidwwilson(AT)comcast.net), Apr 14 2003
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MATHEMATICA
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a[1]=1; p[1]={2}; a[n_] := Module[{k, new}, For[k=a[n-1]+1, Intersection[p[n-1], (new=Select[(a/@Range[n-1])+k, PrimeQ])]!={}, k++, Null]; p[n]=Union[p[n-1], new]; a[n]=k];
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PROGRAM
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(PARI) v=vector(1000):v[1]=1:vv=vector(1000):vv[1]=1:n=1:while(n<100, n=n+1:for(m=1, 10^9, f=0: if(!vv[m], v[n]=m:w=vector(1000):for(k=2, n, for(l=1, k-1, s=v[k]+v[l]: if(isprime(s), if(w[s], f=1:break, w[s]=1))): if(f, break)): if(!f, print1(m", "):vv[m]=1:break))))
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CROSSREFS
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A082929 lists primes not of the form a(i)+a(j). A082930 lists even terms. Cf. A082931.
Sequence in context: A073301 A028756 A028799 this_sequence A108330 A039892 A105404
Adjacent sequences: A080432 A080433 A080434 this_sequence A080436 A080437 A080438
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 20 2003
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EXTENSIONS
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Corrected and extended by Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 14 2003
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