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A175933 Number of ways of writing n=p+k with p a prime number and k a primorial number. 6
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A293900 A284463 A169758 * A175940 A299236 A353970
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(85), a(89), etc. corrected by R. J. Mathar, Oct 25 2010
STATUS
approved

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Last modified April 16 16:48 EDT 2024. Contains 371749 sequences. (Running on oeis4.)