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%I #24 Sep 08 2022 08:45:55
%S 4,5,6,9,12,14,17,19,24,26,28,29,33,34,39,40,44,47,49,50,54,59,61,64,
%T 68,69,72,74,75,79,82,83,84,89,94,96,99,103,104,105,109,110,114,116,
%U 117,119,124,127,129,131,134,138,139,144,145,149,152,154,159,160,164
%N Numbers of the form 5k + 4, 7k + 5, or 11k + 6.
%C Numbers such that the Ramanujan congruences apply, making p(a(n)) divisible by at least one of 5, 7, or 11, where p is A000041.
%C Union of A016897, A017041 and A017461.
%C First differences are periodic with period length 145.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Ramanujan's_congruences">Ramanujan's congruences</a>
%H <a href="/index/Rec#order_146">Index entries for linear recurrences with constant coefficients</a>, order 146.
%F a(n) = a(n-145) + 385 = a(n-1) + a(n-145) - a(n-146).
%t Union[With[{no=30},Join[5Range[0,no]+4,7Range[0,no]+5,11Range[0,no]+6]]] (* _Harvey P. Dale_, Feb 18 2011 *)
%o (Magma) IsA182719:=func< n | exists{ k: k in [0..n div 5] | n in [5*k+4, 7*k+5, 11*k+6] } >; [ n: n in [1..160] | IsA182719(n) ]; // _Klaus Brockhaus_, Feb 08 2011
%Y Cf. A000041, A016897, A017041, A017461.
%K nonn,easy
%O 1,1
%A _Omar E. Pol_, Feb 08 2011
%E Rewritten by _Charles R Greathouse IV_ and _Klaus Brockhaus_, Feb 08 2011