A172469 Primes congruent to +/-1 or +/-7 modulo 25.

7, 43, 101, 107, 149, 151, 157, 193, 199, 251, 257, 293, 307, 349, 401, 443, 449, 457, 499, 557, 593, 599, 601, 607, 643, 701, 743, 751, 757, 857, 907, 1049, 1051, 1093, 1151, 1193, 1201, 1249, 1301, 1307, 1399, 1451, 1493, 1499, 1543, 1549, 1601, 1607

Offset

1,1

Comments

Equivalently, primes p such that the smallest extension of F_p containing the 5th roots of unity also contains the 25th roots of unity.

In this respect, the sequence is the n=5 instance of a family of sequences. For n=3, see A129805, and for n=2, see A002144.

Equivalently, the primes p for which, if p^t = 1 mod 5, then p^t = 1 mod 25.

Links

Table of n, a(n) for n=1..48.

Formula

A141927 U A141932 U A141946 U A141941. [From R. J. Mathar, Feb 05 2010]

Prog

(Python)
from itertools import count, islice
from sympy import isprime
def A172469_gen(): # generator of terms
    yield from (7, 43)
    for n in count(50, 50):
        for m in (1, 7, 43, 49):
            if isprime(n+m):
                yield n+m
A172469_list = list(islice(A172469_gen(), 48)) # Chai Wah Wu, Apr 28 2025

Crossrefs

Sequence in context: A297306 A247949 A031914 * A216301 A201717 A134154

Adjacent sequences: A172466 A172467 A172468 * A172470 A172471 A172472

Keyword

easy,nonn

Author

Katherine E. Stange, Feb 03 2010

Extensions

More terms from R. J. Mathar, Feb 05 2010

Status

approved