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A210499
Primes p of the form 1 mod 4 such that p+1 has a prime factor of the form 1 mod 4.
1
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
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
KEYWORD
nonn
AUTHOR
Jon Perry, Jan 25 2013
STATUS
approved