A175933 Number of ways of writing n=p+k with p a prime number and k a primorial number.

0, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 0, 2, 1, 1, 0, 1, 1, 3, 1, 1, 0, 2, 1, 3, 0, 0, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 3, 1, 1, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 0, 0, 0, 2, 1, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 3, 1, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 24 2010

Keywords

• nonn

Comments

Number of partitions of n into the sum of a prime number and a primorial number. Number of decompositions of n into an unordered sum of a prime number and a primorial number.

For n through small powers of 10, the range of partition values seen is about log_10(n)+2. - Bill McEachen, Jan 07 2016

Examples

			a(4)=2 because 4(natural) = 2(prime)+2(primorial) = 3(prime)+1(primorial).
		

Links

• Bill McEachen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A062602, A129363.

Programs

Maple

A002110 := proc(n) option remember; if n = 0 then 1; else mul( ithprime(k),k=1..n) ; end if; end proc:
A175933 := proc(n) a := 0 ; for k from 0 do p := A002110(k) ; if p +2 > n then return a; elif isprime(n-p) then a := a+1 ; end if; end do: end proc:
seq(A175933(n),n=1..120) ; # R. J. Mathar, Oct 25 2010

Mathematica

t = Table[Product[Prime@ k, {k, n}], {n, 0, 5}]; Table[Count[Map[First, Function[k, Transpose@ {k - #, #} &@ Prime@ Range@ PrimePi@ k]@ n], x_ /; MemberQ[t, x]], {n, 120}]  (* Michael De Vlieger, Jan 09 2016 *)

PARI

lyst(maxx)={n=1; while (n<=maxx,c=0; q=1; for(i5=0, n, if(i5>0, q=q*prime(i5)); if(q>n-2,break); z=truncate(q); if(isprime(n-z),c++)); print1(c,","); n+=1);} \\ Bill McEachen, Jan 07 2016

PARI

A175933(n,p=1,k=1,c=0)={until(2>n-k*=p=nextprime(p+1),isprime(n-k)&&c++);c} \\ M. F. Hasler, Jan 21 2016

Extensions

a(85), a(89), etc. corrected by R. J. Mathar, Oct 25 2010