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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).

%I A355697 #80 Sep 21 2022 12:00:17
%S A355697 0,1,3,4,6,9,13,16,20,25,31,36,42,49,57,66,76,87,99,112,126,141,157,
%T A355697 172,188,205,223,240,258,277,295,314,334,355,377,400,424,449,473,498,
%U A355697 524,551,579,608,638,669,701,732,764,797,829,860,892,925,959,994,1030,1067,1105,1144,1184
%N 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).
%H A355697 John Tyler Rascoe, <a href="/A355697/a355697.jpg">Illustration of first 15 terms</a>
%e A355697 0                              =  0
%e A355697 0 + 1                          =  1
%e A355697 0 + 1 + 2                      =  3 (prime)
%e A355697 0 + 1 + 2 + 1                  =  4
%e A355697 0 + 1 + 2 + 1 + 2              =  6
%e A355697 0 + 1 + 2 + 1 + 2 + 3          =  9
%e A355697 0 + 1 + 2 + 1 + 2 + 3 + 4      = 13 (prime)
%e A355697 0 + 1 + 2 + 1 + 2 + 3 + 4 + 3  = 16
%t A355697 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 *)
%o A355697 (Python)
%o A355697 import sympy
%o A355697 A355697 = A = [0,1]
%o A355697 for n in range(1,100):
%o A355697       if sympy.isprime(A355697[-1]):
%o A355697             y = A[-1] - A[-2] - 1
%o A355697       else:
%o A355697             y = A[-1] - A[-2] + 1
%o A355697       A.append(A[-1] + y)
%o A355697 (MATLAB)
%o A355697 function a = A355697(max_n)
%o A355697     a = 0; m = 0;
%o A355697     for n = 1:max_n
%o A355697         if isprime(a(n))
%o A355697             m = m - 1;
%o A355697         else
%o A355697             m = m + 1;
%o A355697         end
%o A355697         a(n+1) = a(n) + m;
%o A355697     end
%o A355697 end % _Thomas Scheuerle_, Jul 22 2022
%o A355697 (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
%Y A355697 Cf. A000217, A104589, A116533, A332410, A356445.
%K A355697 nonn,easy
%O A355697 0,3
%A A355697 _John Tyler Rascoe_, Jul 19 2022