A210499 Primes p of the form 1 mod 4 such that p+1 has a prime factor of the form 1 mod 4.

29, 73, 89, 101, 109, 149, 173, 181, 193, 229, 233, 269, 313, 317, 337, 349, 373, 389, 409, 449, 457, 509, 521, 569, 577, 653, 673, 677, 701, 709, 769, 809, 821, 829, 853, 857, 929, 941, 953, 1009, 1013, 1021, 1049, 1069, 1097, 1109, 1117, 1129, 1153, 1181

Offset

1,1

Comments

Vaguely related to odd perfect numbers - they must have one prime 1 mod 4 with an exponent 1 mod 4.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

29 == 1 mod 4 and 29+1 = 30 = 2*3*5 has 5 == 1 mod 4 as a prime factor.

Maple

filter:= proc(n) isprime(n) and has(1, numtheory:-factorset(n+1) mod 4) end proc:
select(filter, [seq(i, i=1..2000, 4)]); # Robert Israel, Mar 13 2020

Mathematica

Select[Prime[Range[500]], Mod[# - 1, 4] == 0 && Sort[Mod[Transpose[FactorInteger[# + 1]][[1]] - 1, 4]][[1]] == 0 &] (* T. D. Noe, Jan 25 2013 *)

Crossrefs

Cf. A000396, A002144, A016813.

Sequence in context: A099775 A139893 A063312 * A161617 A142305 A184072

Adjacent sequences: A210496 A210497 A210498 * A210500 A210501 A210502

Keyword

nonn

Author

Jon Perry, Jan 25 2013

Status

approved