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

1,6

Links

Table of n, a(n) for n=1..79.

Example

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

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 *)

Crossrefs

Cf. A062602, A062610, A167707.

Sequence in context: A224989 A124876 A188901 * A344096 A253138 A283994

Adjacent sequences: A171615 A171616 A171617 * A171619 A171620 A171621

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 13 2009

Extensions

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

Status

approved