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A345727 a(n) = (prime(n)+1) * prime(n+1).

%I A345727 #27 Jan 08 2023 15:07:23
%S A345727 9,20,42,88,156,238,342,460,696,930,1184,1558,1806,2068,2544,3186,
%T A345727 3660,4154,4828,5256,5846,6640,7476,8730,9898,10506,11128,11772,12430,
%U A345727 14478,16768,18084,19182,20860,22650,23864,25754,27388,29064,31146,32580,34762
%N A345727 a(n) = (prime(n)+1) * prime(n+1).
%H A345727 Harvey P. Dale, <a href="/A345727/b345727.txt">Table of n, a(n) for n = 1..1000</a>
%F A345727 a(n) = A008864(n)*A000040(n+1).
%F A345727 a(n) = A180617(n)-A008864(n).
%F A345727 a(n) = A006094(n)+A000040(n+1).
%e A345727 a(1) = (prime(1)+1) * prime(2) = 3 *  3 =  9,
%e A345727 a(2) = (prime(2)+1) * prime(3) = 4 *  5 = 20,
%e A345727 a(3) = (prime(3)+1) * prime(4) = 6 *  7 = 42,
%e A345727 a(4) = (prime(4)+1) * prime(5) = 8 * 11 = 88.
%p A345727 A345727 := proc(n)
%p A345727     (ithprime(n)+1)*ithprime(n+1) ;
%p A345727 end proc:
%p A345727 seq(A345727(n),n=1..10) ; # _R. J. Mathar_, Aug 16 2021
%t A345727 (Prime@#+1)Prime[#+1]&/@Range@50 (* _Giorgos Kalogeropoulos_, Jul 23 2021 *)
%t A345727 (#[[1]]+1)#[[2]]&/@Partition[Prime[Range[50]],2,1] (* _Harvey P. Dale_, Jan 08 2023 *)
%o A345727 (PARI) for(n=1, 100, print1((prime(n)+1)*prime(n+1), ", "))
%o A345727 (Ruby) require 'prime'
%o A345727 values = []
%o A345727 primes = Prime.first(20)
%o A345727 primes.each_index do |n|
%o A345727     next if n < 1
%o A345727     values << (primes[n - 1] + 1) * primes[n]
%o A345727 end
%o A345727 p values
%Y A345727 Cf. A000040, A006094, A008864, A123134, A180617.
%K A345727 nonn
%O A345727 1,1
%A A345727 _Simon Strandgaard_, Jul 20 2021