A080435 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.

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

Offset

1,2

Comments

Conjecture: There are infinitely many primes not of the form a(i)+a(j). - David W. Wilson, Apr 14 2003

Are there infinitely many even numbers in the sequence? - David W. Wilson, Apr 14 2003

Links

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Mathematica

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];

Prog

(PARI) v=vector(1000); print1(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))))

Crossrefs

A082929 lists primes not of the form a(i)+a(j). A082930 lists even terms. Cf. A082931.

Sequence in context: A073301 A028756 A028799 * A108330 A262587 A328724

Adjacent sequences: A080432 A080433 A080434 * A080436 A080437 A080438

Keyword

nonn

Author

Amarnath Murthy, Feb 20 2003

Extensions

Corrected and extended by Ralf Stephan, Apr 14 2003

Status

approved