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a(n) is the prime before A262275(n).
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%I #33 Dec 21 2022 21:38:36

%S 2,7,13,37,61,79,107,113,151,181,199,239,271,281,349,359,397,457,503,

%T 541,557,577,613,733,769,787,857,863,953,983,1021,1061,1069,1163,1193,

%U 1213,1399,1429,1439,1459,1493,1583,1619,1667,1721,1733,1811,1907,2017,2053

%N a(n) is the prime before A262275(n).

%C The sum of the individual gaps formed by the subtraction of the next lower prime number from each prime in A262275 approximates the prime counting function at very large n.

%D Michael P. May, "Relationship Between the Prime Counting Function and a Unique Prime Number Sequence", accepted for publication in the March 2023 edition of the Missouri Journal of Mathematical Sciences.

%F a(n) = A262275(n) - A348677(n).

%F a(n) = A151799(A262275(n)).

%e a(3) = A262275(3) - A348677(3) = 17 - 4 = 13.

%o (PARI) b(n) = {my(k=0); while(isprime(n), k++; n=primepi(n)); k};

%o apply(x->precprime(x-1), apply(prime, select(n->b(n)%2, [1..500]))) \\ _Michel Marcus_, Nov 18 2022

%Y Cf. A151799, A262275, A348677.

%K nonn

%O 1,1

%A _Michael P. May_, Nov 11 2022