A393868 Runs of consecutive odd/even terms in A393866.

2, 4, 2, 4, 8, 2, 6, 4, 10, 6, 4, 2, 2, 2, 4, 4, 2, 2, 6, 2, 2, 2, 8, 2, 2, 4, 2, 6, 2, 12, 2, 2, 2, 6, 8, 2, 8, 4, 4, 2, 2, 2, 2, 2, 6, 4, 6, 2, 2, 4, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 4, 6, 2, 2, 4, 2, 2, 4, 2, 2, 4, 6, 2, 2, 2, 6, 4, 4, 2, 2, 2, 6, 4, 2, 2, 2, 2, 4, 6, 6, 2, 4, 6, 2, 8, 2, 4, 4, 2, 8, 2, 10, 4, 8, 2, 4, 16

Offset

1,1

Comments

It appears that all terms are even.

Let F(x) be the g.f. of A393866, then [x^n] F(x)^prime(n) * (1 - prime(n)*x) = 0 for n >= 1.

Links

Paul D. Hanna, Table of n, a(n) for n = 1..272

Example

The parity of A393866 begins [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, ...];
so, the runs of odd/even terms in A393866 begin: 2 odd, 4 even, 2 odd, 4 even, 8 odd, 2 even, 6 odd, 4 even, 10 odd, ...
The g.f. of A393866 begins
F(x) = 1 + x + 2*x^2 + 10*x^3 + 82*x^4 + 1610*x^5 + 21103*x^6 + 557487*x^7 + 10593462*x^8 + ...
where [x^n] F(x)^prime(n) * (1 - prime(n)*x) = 0 for n >= 1.

Prog

(PARI) \\ Generate N terms of A393866 as vector A
N=300; print1("Generating ", N, " terms of A393866"); A=[1]; for(n=2, N+1, A=concat(A, 0); V=Vec(Ser(A)^prime(n-1)); A[#A] = V[#A-1] - V[#A]/prime(n-1); print1(".") );
\\ Count runs of odd/even terms in A393866
r=1; for(n=1, #A-1, if((A[n+1]%2)==(A[n]%2), r=r+1, print1(r, ", "); r=1))

Crossrefs

Cf. A393866.

Sequence in context: A112791 A227346 A296141 * A286536 A318768 A166242

Adjacent sequences: A393865 A393866 A393867 * A393869 A393870 A393871

Keyword

nonn

Author

Paul D. Hanna, Mar 29 2026

Status

approved