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
EXAMPLE
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
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