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A227432

Difference between 10^n and the first prime of gap 4 > 10^n.

3, 3, 9, 99, 189, 33, 453, 123, 93, 597, 69, 189, 279, 1173, 399, 1719, 2733, 2493, 87, 753, 213, 537, 249, 663, 3309, 123, 279, 597, 2253, 2853, 3237, 2403, 6747, 1257, 3069, 159, 3933, 2277, 6057, 7557, 1869, 17043, 2463, 17013, 4923, 4767, 15723, 2607, 2763

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OFFSET

1,1

COMMENTS

As N increases, the ratio sum(a(n)/n^2)/N for n = 1 to N tends to 4.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..272

EXAMPLE

10^1+3 = 13, 13 and 17 primes of gap 4, a(1)=3.

10^2+3 = 103, 103 and 107 primes of gap 4, a(2)=3.

PROG

(PARI) a(n) = {p = nextprime(10^n); q = nextprime(p+1); while (q-p != 4, r = nextprime(q+1); p = q; q = r); p - 10^n; } \\ Michel Marcus, Feb 24 2018