A103781 Sum of any four successive terms is prime, a(1)=a(2)=0,a(3)=1.

0, 0, 1, 1, 1, 2, 3, 5, 3, 6, 5, 9, 9, 8, 11, 13, 11, 12, 17, 19, 13, 18, 21, 21, 19, 22, 27, 29, 23, 24, 31, 31, 27, 38, 35, 37, 29, 48, 37, 43, 35, 52, 43, 49, 37, 62, 45, 53, 39, 74, 57, 57, 41, 78, 63, 59, 51, 84, 69, 65, 53, 90, 73, 67, 63, 104, 77, 69, 67, 118, 83, 79, 69

Offset: 1

Author

Zak Seidov, Feb 15 2005

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A073737, A083242.

Programs

Mathematica

(*seed*)b4 = {0, 0, 1}; Do[x = Prime[n] - (b4[[ -1]] + b4[[ -2]] + b4[[ -3]]); b4 = Append[b4, x], {n, 1, 200}]; b4
nxt[{a_, b_, c_}] := {b, c, NextPrime[a + b + c] - (a+b + c)}; NestList[nxt, {0, 0, 1}, 100][[All, 1]] (* Harvey P. Dale, Sep 20 2022 *)

Formula

a(n) = A000040(n-3) - a(n-1) - a(n-2) - a(n-3). - Jason Yuen, Sep 01 2024