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A139783 Quadruple lucky numbers (lower terms). Numbers n such that n, n+2, n+6, n+8 are all Lucky numbers.

%I A139783 #13 Feb 16 2025 08:33:08
%S A139783 1,7,67,127,613,925,1495,1765,2209,2815,3403,5965,6661,8827,9115,
%T A139783 15229,16387,18145,19153,21925,23563,24637,27031,27199,28987,31381,
%U A139783 32635,34717,35701,36673,40447,43225,43975,47419,50317,51157,56263,64495
%N A139783 Quadruple lucky numbers (lower terms). Numbers n such that n, n+2, n+6, n+8 are all Lucky numbers.
%C A139783 Weisstein comments: "the frequency of twin primes and twin lucky numbers are similar." This is to lucky numbers A000959 and A031158 Twin lucky numbers (lower terms) as prime numbers A000040 and A001359 Lesser of twin primes are to A007530 Prime quadruples: numbers n such that n, n+2, n+6, n+8 are all prime.
%H A139783 Amiram Eldar, <a href="/A139783/b139783.txt">Table of n, a(n) for n = 1..10000</a>
%H A139783 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/LuckyNumber.html">Lucky Number.</a>
%F A139783 a(n) = {k such that k is in A000959 and k+2 is in A000959 and k+6 is in A000959 and k+8 is in A000959} = {k such that k is in A031158 and k+6 is in A031158}.
%e A139783 a(1) = 1 because 1, 1+2=3, 1+6=7 and 1+8=9 are all lucky numbers A000959.
%e A139783 a(2) = 7 because 7, 7+2=9, 7+6=13 and 7+8=15 are all lucky numbers A000959.
%e A139783 a(3) = 67 because {67, 69, 73, 75} are all lucky numbers.
%e A139783 a(4) = 127 because {127, 129, 133, 135} are all lucky numbers.
%e A139783 a(5) = 613 because {613, 615, 619, 621} are all lucky numbers.
%e A139783 a(6) = 925 because {925, 927, 931, 933} are all lucky numbers.
%e A139783 a(7) = 1495 because {1495, 1497, 1501, 1503} are all lucky numbers.
%Y A139783 Cf. A000040, A000959, A001359, A031158.
%K A139783 easy,nonn
%O A139783 1,2
%A A139783 _Jonathan Vos Post_, May 20 2008
%E A139783 Inserted a(8)=1765 and extended, _R. J. Mathar_, Jul 18 2008