This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A068873 #51 May 12 2025 15:58:40
%S A068873 2,5,19,17,43,41,79,83,127,131,199,197,283,281,379,389,499,509,643,
%T A068873 641,809,809,983,971,1171,1163,1381,1373,1609,1607,1861,1861,2137,
%U A068873 2137,2437,2441,2749,2767,3109,3109,3457,3457,3833,3847,4243,4241,4663,4679,5119
%N A068873 Smallest prime which is a sum of n distinct primes.
%C A068873 Conjectured terms a(50)-a(76): 5147, 5623, 5591, 6079, 6101, 6599, 6607, 7151, 7151, 7699, 7699, 8273, 8293, 8893, 8893, 9521, 9547, 10211, 10223, 10889, 10891, 11597, 11617, 12343, 12373, 13099, 13127. - _Jean-François Alcover_, Apr 22 2020
%D A068873 Shantanu Dey & Moloy De, Two conjectures on prime numbers, Journal of Recreational Mathematics, Vol. 36 (3), pp 205-206. Baywood Publ. Co, Amityville NY 2011.
%H A068873 David A. Corneth, <a href="/A068873/b068873.txt">Table of n, a(n) for n = 1..10000</a> (first 200 terms from Jean-François Alcover)
%H A068873 Jean-François Alcover, <a href="/A068873/a068873.txt">Conjectured terms up to a(200).</a>
%F A068873 Min(a(n), A073619(n)) = A007504(n) for n > 1. - _Jonathan Sondow_, Jul 10 2012
%e A068873 a(3) = 19 as 19 is the smallest prime which can be expressed as the sum of three primes as 19 = 3 + 5 + 11.
%e A068873 a(4) = 17= 2+3+5+7. a(2)=A038609(1). a(3)=A124867(7). Further examples in A102330.
%p A068873 # Number of ways to write n as a sum of k distinct primes, the smallest
%p A068873 # being smalp
%p A068873 sumkprims := proc(n,k,smalp)
%p A068873 option remember;
%p A068873 local a,res,pn;
%p A068873 res := n-smalp ;
%p A068873 if res < 0 then
%p A068873 return 0;
%p A068873 elif res > 0 and k <=0 then
%p A068873 return 0;
%p A068873 elif res = 0 and k = 1 then
%p A068873 return 1;
%p A068873 else
%p A068873 pn := nextprime(smalp) ;
%p A068873 a := 0 ;
%p A068873 while pn <= res do
%p A068873 a := a+procname(res,k-1,pn) ;
%p A068873 pn := nextprime(pn) ;
%p A068873 end do:
%p A068873 a ;
%p A068873 end if;
%p A068873 end proc:
%p A068873 # Number of ways of writing n as a sum of k distinct primes
%p A068873 A000586k := proc(n,k)
%p A068873 local a,i,smalp ;
%p A068873 a := 0 ;
%p A068873 for i from 1 do
%p A068873 smalp := ithprime(i) ;
%p A068873 if k*smalp > n then
%p A068873 return a;
%p A068873 end if;
%p A068873 a := a+sumkprims(n,k,smalp) ;
%p A068873 end do:
%p A068873 end proc:
%p A068873 # Smallest prime which is a sum of n distinct primes
%p A068873 A068873 := proc(n)
%p A068873 local a,i;
%p A068873 a := A007504(n) ;
%p A068873 a := nextprime(a-1) ;
%p A068873 for i from 1 do
%p A068873 if A000586k(a,n) > 0 then
%p A068873 return a;
%p A068873 end if;
%p A068873 a := nextprime(a) ;
%p A068873 end do:
%p A068873 end proc: # _R. J. Mathar_, May 04 2014
%o A068873 (PARI) a(n)=
%o A068873 {
%o A068873 my(P=primes(n), k=n, t, res = oo);
%o A068873 while(1,
%o A068873 forvec(v=vector(n-1, i, [1, k-1]),
%o A068873 t=sum(i=1, n-1, P[v[i]])+P[k];
%o A068873 if(isprime(t),
%o A068873 res = min(res, t);
%o A068873 )
%o A068873 ,
%o A068873 2 \\ flag: only strictly increasing vectors v
%o A068873 );
%o A068873 P=concat(P, nextprime(P[k]+1));
%o A068873 k++;
%o A068873 if(P[k] + sum(i = 1+bitand(n,1), n-1+bitand(n,1), P[i]) > res,
%o A068873 return(res)
%o A068873 )
%o A068873 );
%o A068873 }
%o A068873 \\ _Charles R Greathouse IV_, Sep 19 2015; corrected by _David A. Corneth_, May 12 2025
%Y A068873 Cf. A102330, A013918, A007504.
%K A068873 nonn
%O A068873 1,1
%A A068873 _Amarnath Murthy_, Mar 19 2002
%E A068873 More terms from _Sascha Kurz_, Feb 03 2003
%E A068873 Corrected by _Ray Chandler_, Feb 02 2005