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%I #11 Oct 25 2022 20:07:48
%S 13,37,157,877,5917,46237,409117,4037917,43954717,522956317,
%T 6749977117,93928268317,1401602636317,22324392524317,378011820620317,
%U 6780385526348317,128425485935180317,2561327494111820317,53652269665821260317,1177652997443428940317
%N a(n) = 13 + Sum_{j=4..n+3} j!.
%C Are there infinitely many terms in the intersection of this sequence and A036570?
%C Answer from _Don Reble_, Mar 25 2016: No, after the ninth term, all terms are multiples of 13.
%H G. C. Greubel, <a href="/A147615/b147615.txt">Table of n, a(n) for n = 0..445</a>
%F a(n) = 13 + !(n+4) - !4 = 13 + A003422(n+4) - A003422(4). - _G. C. Greubel_, Oct 24 2022
%e a(0) = 13, a(1) = 13 + 4!, a(2) = 13 + 4! + 5!, ....
%t A147615[n_]:= 13 +Sum[j!, {j,4,n+3}]; Table[A147615[n], {n,0,30}] (* _G. C. Greubel_, Oct 24 2022 *)
%o (Magma) [n eq 0 select 13 else 13 + (&+[Factorial(j+4): j in [0..n-1]]): n in [0..30]]; // _G. C. Greubel_, Oct 24 2022
%o (SageMath)
%o def A147615(n): return 13 + sum(factorial(j+4) for j in range(n))
%o [A147615(n) for n in range(30)] # _G. C. Greubel_, Oct 24 2022
%Y Cf. A003422, A036570.
%K nonn
%O 0,1
%A Ricky Pollack (rickypollack(AT)gmail.com), Apr 30 2009
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