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%I #37 Oct 04 2020 23:33:29
%S 1,2,4,6,8,10,11,13,15,18,19,21,22,24,26,28,30,32,34,35,36,38,40,42,
%T 45,47,48,50,51,53,55,57,60,61,65,66,67,68,70,72,74,76,77,79,81,82,85,
%U 88,89,91,93,94,95,99,101,102,104,105,106,107,108,112,116,117
%N a(n) = pi(prime(n) - n) + n, where pi is the prime counting function.
%C It can be shown that a(n) > a(n-1) >= 1 and a(n) <= 2*n - 1 < 2*n (see proofs in the Links section).
%H Ya-Ping Lu, <a href="/A334614/a334614.pdf">Proofs of the two observations in the Comments section</a>
%F a(n) = A000720(A014689(n)) + n.
%F a(n) = A065328(n) + n. - _Michel Marcus_, Sep 12 2020
%t Table[PrimePi[Prime[n] - n] + n, {n, 1, 64}] (* _Amiram Eldar_, Sep 09 2020 *)
%o (Python)
%o from sympy import prime, primepi
%o for n in range(1, 100001):
%o a_n = primepi(prime(n) - n) + n
%o print(a_n)
%o (PARI) a(n) = n + primepi(prime(n) - n); \\ _Michel Marcus_, Sep 09 2020
%Y Cf. A000040, A000720, A014688, A014689, A062298, A065328, A097933.
%Y Cf. A332086, A337334.
%K nonn
%O 1,2
%A _Ya-Ping Lu_, Sep 08 2020
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