# A80435

David Wilson davidwwilson at attbi.com
Mon Apr 14 16:20:41 CEST 2003

----- Original Message -----
From: Ralf Stephan
To: seqfan at ext.jussieu.fr
Sent: Monday, April 14, 2003 3:22 AM
Subject: Re: A80435

judmccr wrote
> A80435 seems ambiguous or incorrect.  I wrote to the author asking for a
> clarification 4 days ago, but I haven't gotten a reply.

%S A080435 1,2,3,5,8,15,17
%N A080435 Distinct numbers such that if a(i) + a(j) is a prime p then p is so obtained uniquely (no other pair of members has sum p).

I'd add 'smallest', then I get

? 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))))

1,2,3,5,7,8,13,14,19,20,23,25,27,31,37,43,47,49,50,55,57,61,67,73,75,79,85,91,97,98,103,107,109,111,115,121,127,131,133,135,139,140,145,151,157,163,169,175,181,185,187,193,199,200,205,211,212,217,223,229,235,239,241,245,247,253,259,265,271,273,277,283,289,
***   user interrupt after 4mn, 28,170 ms.

> First, why isn't 7 in the sequence?  Is it because it doesn't yield any new
> primes when summed with the previous terms?  If that is correct, then why
> isn't 14 in the sequence, since it yields 14+3=17?

good questions...

ralf

I confirm Ralf Stephan's values for A080435.  Formatted for input into submission page:

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
163 169 175 181 185 187 193 199 200 205 211 212 217 223 229 235 239 241

The conjecture in the comment is wrong.  I would in fact conjecture that infinitely many
primes do not occur as a sum of a pair of elements of A080435.  The list of such primes
begins

2 79 179 191 211 263 277 313 349 359 409 499 503 509 557 571 599 619 641
647 673 683 739 769 773 809 857 929 941 947 967 997 1019 1039 1049 1069
1091 1097 1103 1129 1151 1201 1229 1289 1301 1399 1429 1451 1487

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