A354030 a(n) = 1 if n is either 1 or a prime power of the form 4m+1, otherwise 0.

1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65539

Index entries for characteristic functions

Formula

For n > 1, a(n) = A174275(n) - A354028(n).

a(n) >= A354031(n).

Example

5, being a Pythagorean prime (A002144), when raised to any power, will always give a number of the form 4m+1, therefore a(1) = a(5) = a(25) = a(125) = 1.
7, although itself a prime of the form 4m+3 (A002145), when raised to an even power will always give a number of the form 4m+1, therefore a(49) = a(2401) = 1.

Prog

(PARI) A354030(n) = ((1==n)||((1==(n%4)) && isprimepower(n)));

Crossrefs

Characteristic function of A085759.

Cf. also A010055, A174275, A354028, A354031.

Sequence in context: A014129 A121505 A014289 * A015297 A015073 A014961

Adjacent sequences: A354027 A354028 A354029 * A354031 A354032 A354033

Keyword

nonn

Author

Antti Karttunen, May 15 2022

Status

approved