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%I #14 Apr 19 2021 17:10:56
%S 2,7,15,31,51,83,119,171,231,307,395,503,627,755,919,1079,1271,1483,
%T 1703,1967,2215,2495,2795,3127,3479,3839,4267,4647,5059,5539,5991,
%U 6511,7063,7651,8211,8855,9439,10139,10887,11611,12371,13159,13951,14715,15647,16591,17431,18487,19419,20415,21491
%N a(n) = Sum_{i=1..n} (prime(i+1)-prime(i))*prime(n+1-i).
%C Convolution of A000040 and A001223.
%H Robert Israel, <a href="/A343531/b343531.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 2*(7-5)+3*(5-3)+5*(3-2) = 15.
%p P:= [seq(ithprime(i),i=1..101)]:
%p G:= P[2..-1]-P[1..-2]:
%p seq(add(P[i]*G[n+1-i],i=1..n),n=1..100)];
%t Table[Sum[(Prime[i + 1] - Prime[i]) Prime[n + 1 - i], {i, n}], {n,
%t 50}] (* _Wesley Ivan Hurt_, Apr 18 2021 *)
%o (PARI) a(n) = sum(i=1, n, (prime(i+1)-prime(i))*prime(n+1-i)); \\ _Michel Marcus_, Apr 19 2021
%Y Cf. A000040, A001223.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Apr 18 2021
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