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A112418 Primes which have a prime number of partitions into five distinct primes. 1
53, 59, 67, 83, 113, 151, 157, 211, 239, 601, 809, 821, 881, 971, 1237, 1297, 1427, 1669, 1759, 1973, 2069, 2129, 2243, 2333, 2659, 2677, 2719, 2789, 2803, 2999, 3329, 3613, 3623, 3769, 3797, 4001, 4451 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000009, A000041, A007963, A051034.

Sequence in context: A095509 A268913 A166385 * A059497 A059472 A165455

Adjacent sequences:  A112415 A112416 A112417 * A112419 A112420 A112421

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

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Last modified April 15 07:23 EDT 2021. Contains 342975 sequences. (Running on oeis4.)