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A286624 a(n) = (prime(1+n)*prime(n)) + prime(n) + 1.

%I A286624 #21 Mar 14 2021 18:43:49
%S A286624 9,19,41,85,155,235,341,457,691,929,1179,1555,1805,2065,2539,3181,
%T A286624 3659,4149,4825,5255,5841,6637,7471,8723,9895,10505,11125,11771,12427,
%U A286624 14465,16765,18079,19181,20851,22649,23859,25749,27385,29059,31141,32579,34753,37055,38215,39401,42189,47265,50845,52211
%N A286624 a(n) = (prime(1+n)*prime(n)) + prime(n) + 1.
%C A286624 9 is the only perfect square in this sequence. - _Altug Alkan_, Jul 01 2017
%H A286624 Antti Karttunen, <a href="/A286624/b286624.txt">Table of n, a(n) for n = 1..10000</a>
%F A286624 a(n) = (A000040(1+n)*A000040(n)) + A000040(n) + 1.
%F A286624 a(n) = 1 + A123134(n).
%F A286624 a(n) = A000040(n) + A023523(1+n).
%t A286624 Array[(#1 #2) + #1 + 1 & @@ Prime[# + {0, 1}] &, 49] (* _Michael De Vlieger_, Mar 14 2021 *)
%o A286624 (Scheme)
%o A286624 (define (A286624 n) (+ (* (A000040 (+ 1 n)) (A000040 n)) (A000040 n) 1))
%o A286624 (define (A286624 n) (+ 1 (* (+ 1 (A000040 (+ 1 n))) (A000040 n))))
%o A286624 (PARI) lista(nn) = forprime(p=2, nn, print1(p*(nextprime(p+1)+1)+1, ", ")); \\ _Altug Alkan_, Jul 01 2017
%Y A286624 Row 6 of A286625 (column 6 of A286623). Column 4 of A328464.
%Y A286624 One more than A123134.
%Y A286624 Cf. A000040, A023523, A180932 (primes in this sequence).
%K A286624 nonn
%O A286624 1,1
%A A286624 _Antti Karttunen_, Jun 28 2017