Journal of Integer Sequences, Vol. 24 (2021), Article 21.10.5 |

Departamento de Matemáticas y Computación

Universidad de La Rioja

Logroño

Spain

**Abstract:**

For fixed positive integers *n*, we study the solution of the equation
*n* = *k* + *p*_{k},
where *p*_{k} denotes the *k*th prime number, by means
of the iterative method

which converges to the solution of the equation, if it exists. We also analyze the equation*n* = *ak* + *bp*_{k}
for fixed integer values
and *b*>0,
and its solution by means of a corresponding iterative method.
The case *a*>0 is somewhat similar to the case *a*=*b*=1,
while for *a*<0 the convergence and usefulness of the method
are less satisfactory.
The paper also includes a study of the dynamics of the iterative methods.

which converges to the solution of the equation, if it exists. We also analyze the equation

(Concerned with sequences A000045 A014688 A259180.)

Received March 21 2021; revised versions received March 23 2021; November 16 2021; November 21 2021.
Published in *Journal of Integer Sequences*,
November 27 2021.

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