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%I #9 May 02 2023 23:57:49
%S 1,0,1,0,1,2,1,0,1,2,1,0,1,2,3,4,3,2,1,0,1,2,1,0,1,2,3,4,3,2,1,0,1,2,
%T 1,0,1,2,3,4,3,2,1,0,1,2,3,4,5,6,5,4,3,2,1,0,1,2,1,0,1,2,3,4,5,6,5,4,
%U 3,2,1,0,1,2,3,4,3,2,1,0,1,2,1,0,1,2,3,4,3,2,1,0,1,2,3
%N Number of numbers k, 1 <= k <= n, such that pi(k) = pi(n-k+1).
%F a(n) = Sum_{k=1..n} [pi(k) = pi(n-k+1)], where pi is the prime counting function (A000720) and [ ] is the Iverson bracket.
%e There are two cases for a(6) due to symmetry, namely k=3: pi(3) = 2 = pi(6-3+1) and k=4: pi(4) = 2 = pi(6-4+1).
%t Table[Sum[KroneckerDelta[PrimePi[n - k + 1], PrimePi[k]], {k, n}], {n, 100}]
%o (PARI) a(n) = sum(k=1, n, primepi(k) == primepi(n-k+1)); \\ _Michel Marcus_, May 01 2023
%Y Cf. A000720.
%K nonn,easy
%O 1,6
%A _Wesley Ivan Hurt_, Apr 30 2023
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