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

1,4

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A002110, A062602, A129363.

Sequence in context: A293900 A284463 A169758 * A175940 A299236 A374076

Adjacent sequences: A175930 A175931 A175932 * A175934 A175935 A175936

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 24 2010

Extensions

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

Status

approved