OFFSET
1,1
COMMENTS
The corresponding numbers of partitions are 2,5,11,29,109,331,379,1091...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..102
EXAMPLE
53 is there because there are 2 partitions of 53 (3+7+11+13+19, 5+7+11+13+17) and 2 is prime.
MAPLE
part5_prime:=proc(N) s:=1; for n from 2 to N do cont:=0; for i from 1 to n-5 do for j from i+1 to n-4 do for k from j+1 to n-3 do for l from k+1 to n-2 do for m from l+1 to n-1 do if(ithprime(n)= ithprime(i)+ithprime(j)+ithprime(k)+ithprime(l)+ithprime(m) then cont:=cont+1; fi; od; od; od; od; od; if (isprime(cont)=true) then a[s]:=ithprime(n); s:=s+1; fi; od; end:
PROG
(PARI) has(n)=my(t, Q, R, S); forprime(p=n\5+1, n-26, Q=n-p; forprime(q=Q\4+1, min(p-1, Q-15), R=Q-q; forprime(r=R\3+1, min(q-1, R-8), S=R-r; forprime(s=S-r+1, (S-1)\2, isprime(S-s) && t++)))); isprime(t)
select(has, primes(100)) \\ Charles R Greathouse IV, Apr 22 2015
(PARI) list(lim)=my(v=vectorsmall(precprime(lim)), u=List(), Q, R, S); forprime(p=13, #v-26, Q=#v-p; forprime(q=11, min(p-1, Q-15), R=Q-q; forprime(r=7, min(q-1, R-8), S=R-r; forprime(s=5, min(S-2, r-1), forprime(t=3, min(S-s, s-1), v[p+q+r+s+t]++))))); forprime(p=2, lim, if(isprime(v[p]), listput(u, p))); Set(u) \\ Charles R Greathouse IV, Apr 22 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti and Paolo P. Lava, Dec 09 2005
EXTENSIONS
Edited by Don Reble, Jan 26 2006
a(31)-a(37) from Charles R Greathouse IV, Apr 22 2015
STATUS
approved