A355697 a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-1) + g - 1 if a(n-1) is prime, otherwise a(n) = a(n-1) + g + 1, where g = a(n-1) - a(n-2).

0, 1, 3, 4, 6, 9, 13, 16, 20, 25, 31, 36, 42, 49, 57, 66, 76, 87, 99, 112, 126, 141, 157, 172, 188, 205, 223, 240, 258, 277, 295, 314, 334, 355, 377, 400, 424, 449, 473, 498, 524, 551, 579, 608, 638, 669, 701, 732, 764, 797, 829, 860, 892, 925, 959, 994, 1030, 1067, 1105, 1144, 1184

Offset: 0

Author

John Tyler Rascoe, Jul 19 2022

Keywords

• nonn
• easy

Examples

			0                              =  0
0 + 1                          =  1
0 + 1 + 2                      =  3 (prime)
0 + 1 + 2 + 1                  =  4
0 + 1 + 2 + 1 + 2              =  6
0 + 1 + 2 + 1 + 2 + 3          =  9
0 + 1 + 2 + 1 + 2 + 3 + 4      = 13 (prime)
0 + 1 + 2 + 1 + 2 + 3 + 4 + 3  = 16
		

Links

• John Tyler Rascoe, Illustration of first 15 terms

Crossrefs

Cf. A000217, A104589, A116533, A332410, A356445.

Programs

MATLAB

function a = A355697(max_n)
    a = 0; m = 0;
    for n = 1:max_n
        if isprime(a(n))
            m = m - 1;
        else
            m = m + 1;
        end
        a(n+1) = a(n) + m;
    end
end % Thomas Scheuerle, Jul 22 2022

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = 2*a[n - 1] - a[n - 2] - If[PrimeQ[a[n - 1]], 1, -1]; Array[a, 50, 0] (* Amiram Eldar, Jul 23 2022 *)

PARI

lista(nn) = my(va = vector(nn)); va[1] = 0; va[2] = 1; for (n=3, nn, if (isprime(va[n-1]), va[n] = 2*va[n-1]-va[n-2]-1, va[n] = 2*va[n-1]-va[n-2]+1);); va; \\ Michel Marcus, Aug 23 2022

Python

import sympy
A355697 = A = [0,1]
for n in range(1,100):
      if sympy.isprime(A355697[-1]):
            y = A[-1] - A[-2] - 1
      else:
            y = A[-1] - A[-2] + 1
      A.append(A[-1] + y)