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 A068873 Smallest prime which is a sum of n distinct primes. 8
 2, 5, 19, 17, 43, 41, 79, 83, 127, 131, 199, 197, 283, 281, 379, 389, 499, 509, 643, 641, 809, 809, 983, 971, 1171, 1163, 1381, 1373, 1609, 1607, 1861, 1861, 2137, 2137, 2437, 2441, 2749, 2767, 3109, 3109, 3457, 3457, 3833, 3847, 4243, 4241, 4663, 4679, 5119 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES 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. LINKS Jean-François Alcover, Conjectured terms up to a(200). FORMULA Min(a(n), A073619(n)) = A007504(n) for n > 1. - Jonathan Sondow, Jul 10 2012 EXAMPLE a(3) = 19 as 19 is the smallest prime which can be expressed as the sum of three primes as 19 = 3 + 5 + 11. a(4) = 17= 2+3+5+7. a(2)=A038609(1). a(3)=A124867(7). Further examples in A102330. MAPLE # Number of ways to write n as a sum of k distinct primes, the smallest # being smalp sumkprims := proc(n, k, smalp)     option remember;     local a, res, pn;     res := n-smalp ;     if res < 0 then         return 0;     elif res > 0 and k <=0 then         return 0;     elif res = 0 and k = 1 then         return 1;     else         pn := nextprime(smalp) ;         a := 0 ;         while pn <= res do             a := a+procname(res, k-1, pn) ;             pn := nextprime(pn) ;         end do:         a ;     end if; end proc: # Number of ways of writing n as a sum of k distinct primes A000586k := proc(n, k)     local a, i, smalp ;     a := 0 ;     for i from 1 do         smalp := ithprime(i) ;         if k*smalp > n then             return a;         end if;         a := a+sumkprims(n, k, smalp) ;     end do: end proc: # Smallest prime which is a sum of n distinct primes A068873 := proc(n)     local a, i;     a := A007504(n) ;     a := nextprime(a-1) ;     for i from 1 do         if A000586k(a, n) > 0 then             return a;         end if;         a := nextprime(a) ;     end do: end proc: # R. J. Mathar, May 04 2014 PROG (PARI) a(n)= {     my(P=primes(n), k=n, t);     while(1,         forvec(v=vector(n-1, i, [1, k-1]),             t=sum(i=1, n-1, P[v[i]])+P[k];             if(isprime(t), return(t))         ,             2 \\ flag: only strictly increasing vectors v         );         P=concat(P, nextprime(P[k]+1));         k++     ); } \\ Charles R Greathouse IV, Sep 19 2015 CROSSREFS Cf. A102330, A013918, A007504. Sequence in context: A062097 A323706 A125765 * A035091 A045367 A045368 Adjacent sequences:  A068870 A068871 A068872 * A068874 A068875 A068876 KEYWORD nonn AUTHOR Amarnath Murthy, Mar 19 2002 EXTENSIONS More terms from Sascha Kurz, Feb 03 2003 Corrected by Ray Chandler, Feb 02 2005 STATUS approved

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Last modified May 20 13:02 EDT 2022. Contains 353873 sequences. (Running on oeis4.)