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A068873
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Smallest prime which is a sum of n distinct primes.
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8
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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
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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# 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
local a, i;
a := nextprime(a-1) ;
for i from 1 do
if A000586k(a, n) > 0 then
return a;
end if;
a := nextprime(a) ;
end do:
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PROG
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(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++
);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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