A171618 Number of ways of writing n=k1+k2 with k1 and k2 in A167707.

1, 1, 1, 1, 1, 2, 1, 3, 2, 4, 3, 3, 3, 5, 4, 6, 5, 6, 5, 7, 6, 8, 6, 8, 8, 8, 9, 9, 10, 10, 9, 11, 10, 12, 12, 13, 11, 12, 13, 13, 15, 14, 14, 15, 14, 16, 14, 17, 17, 16, 17, 17, 18, 18, 19, 18, 19, 19, 21, 21, 19, 21, 20, 22, 24, 23, 22, 22, 23, 24, 25, 25, 24, 25, 24, 27, 26, 28, 27

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 13 2009

Keywords

• nonn

Examples

			a(31)=9 because 31 = 0 + 31 = 3 + 28 = 5 + 26 = 7 + 24 = 9 + 22 = 10 + 21 = 11 + 20 = 14 + 17 = 15 + 16.
		

Crossrefs

Cf. A062602, A062610, A167707.

Programs

Maple

isA001097 := proc(n) isprime(n) and (isprime(n+2) or isprime(n-2)) ; end proc:
isA164276 := proc(n) not isprime(n) and ( not isprime(n+1) or not isprime(n-1) ) ; end proc: isA167707 := proc(n) isA001097(n) or isA164276(n) ; end proc:
A167707 := proc(n) option remember; if n = 1 then 0; else for a from procname(n-1)+1 do if isA167707(a) then return a; end if; end do; end if; end proc:
A171618 := proc(n) a := 0 ; for i from 1 do p := A167707(i) ; q := n-p ; if q < p then return a ; end if; if isA167707(q) then a := a+1 ; end if; if q <= p then return a ; end if; end do: end proc:
seq(A171618(n),n=1..120) ; # R. J. Mathar, May 22 2010

Mathematica

isA001097[n_] := PrimeQ[n] && (PrimeQ[n+2] || PrimeQ[n-2]);
isA164276[n_] := !PrimeQ[n] && (!PrimeQ[n+1] ||!PrimeQ[n-1]);
isA167707[n_] := isA001097[n] || isA164276[n];
A167707[n_] := A167707[n] = If[n == 1, 0, For[a = A167707[n-1]+1, True, a++, If[isA167707[a], Return@a]]];
A171618[n_] := Module[{a}, a = 0; For[i = 1, True, i++, p = A167707[i]; q = n-p; If[q < p, Return@a]; If[isA167707[q], a++]; If[q <= p, Return@a]]];
Table[A171618[n], {n, 1, 120}] (* Jean-François Alcover, Feb 23 2024, after R. J. Mathar *)

Extensions

a(29) and a(34) corrected and sequence extended by R. J. Mathar, May 22 2010