The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A269354 Numbers n such that 10n - 3, 10n - 1, 10n + 1 and 10n + 3 are divisible only by primes congruent to 3 mod 4. 1
8, 13, 21, 44, 50, 75, 89, 99, 133, 146, 150, 245, 254, 289, 319, 327, 395, 468, 500, 517, 579, 601, 608, 691, 704, 761, 764, 878, 1011, 1098, 1125, 1199, 1266, 1298, 1313, 1315, 1414, 1495, 1544, 1716, 1723, 1752, 1762, 1781, 1844, 2043, 2073, 2186, 2281, 2291, 2309, 2360, 2444, 2455, 2457 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Primes: 13, 89, 601, 691, 761, 1723, 2281, 2309, 2693, 5437, 5821, 6199, ...
LINKS
EXAMPLE
8 is in this sequence because 10*8 - 3 = 77 = 7*11, 10*8 - 1 = 79, 10*8 + 1 = 81 = 3^4 and 10*8 + 3 = 83 are divisible only primes congruent to 3 mod 4.
MAPLE
filter:= n ->
andmap(t -> numtheory:-factorset(t) mod 4 = {3}, [10*n-3, 10*n-1, 10*n+1, 10*n+3]):
select(filter, [$1..10000]); # Robert Israel, Feb 25 2016
MATHEMATICA
pc3m4Q[n_]:=AllTrue[Flatten[FactorInteger[10 n+{-3, -1, 1, 3}], 1][[All, 1]], Mod[#, 4]==3&]; Select[Range[2500], pc3m4Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 30 2018 *)
PROG
(Magma) [n : n in [1..3000] | forall{d: d in PrimeDivisors(10*n-3) | d mod 4 eq 3] and forall{d: d in PrimeDivisors(10*n-1) | d mod 4 eq 3}
and forall{d: d in PrimeDivisors(10*n+1) | d mod 4 eq 3}
and forall{d: d in PrimeDivisors(10*n+3) | d mod 4 eq 3}] ;
CROSSREFS
Cf. A004614.
Sequence in context: A063849 A273980 A101642 * A195984 A019535 A229446
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 20:03 EDT 2024. Contains 373464 sequences. (Running on oeis4.)