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 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 Harvey P. Dale, Table of n, a(n) for n = 1..1000 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 Adjacent sequences: A269351 A269352 A269353 * A269355 A269356 A269357 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Dec 23 2015 STATUS approved

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