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%I #15 Jan 14 2024 12:28:58
%S 2519,11879,13320,14399,15840,25200,27719,27720,30239,39599,41040,
%T 42119,43560,52920,55439,55440,57959,67319,68760,69839,71280,80640,
%U 83159,83160,85679,95039,96480,97559,99000,108360,110879,110880,113399,122759
%N Numbers n where either n or n+1 is divisible by the numbers from 1 to 12.
%C Equivalent to numbers n where either n or n+1 is divisible by the numbers from 7 to 12. n is a term if n or n+1 is a multiple of 27720. - _Chai Wah Wu_, Jun 15 2020
%H Chai Wah Wu, <a href="/A131662/b131662.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjectures from _Colin Barker_, Jun 15 2020: (Start)
%F G.f.: x*(2519 + 9360*x + 1441*x^2 + 1079*x^3 + 1441*x^4 + 9360*x^5 + 2519*x^6 + x^7) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)).
%F a(n) = a(n-1) + a(n-8) - a(n-9) for n>9. (End)
%e 2519 = 11*229 and 2520 = 2^3*3^2*5*7; that is, 2520 is divisible by all number from 1 to 12 except 11, while 2519 is divisible by 11.
%t Select[Range[150000], Mod[ #, 8]*Mod[ # + 1, 8] == 0 && Mod[ #, 9]*Mod[ # + 1, 9] == 0 && Mod[ #, 5]*Mod[ # + 1, 5] == 0 && Mod[ #, 7]*Mod[ # + 1, 7] == 0 && Mod[ #, 8]*Mod[ # + 1, 8] == 0 && Mod[ #, 12]*Mod[ # + 1, 12] == 0 && Mod[ #, 10]*Mod[ # + 1, 10] == 0 && Mod[ #, 11]*Mod[ # + 1, 11] == 0 &]
%o (Python)
%o A131662_list, n = [], 12
%o while len(A131662_list) < 10000:
%o for i in range(7,12):
%o if (n-1) % i and n % i:
%o break
%o else:
%o A131662_list.append(n-1)
%o for i in range(7,12):
%o if n % i and (n+1) % i:
%o break
%o else:
%o A131662_list.append(n)
%o n += 12 # _Chai Wah Wu_, Jun 15 2020
%K nonn,easy
%O 1,1
%A _Tanya Khovanova_, Sep 13 2007
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