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a:= n-> (t->((p, q)->`if`(q-t<t-p, q, p)-t)(`if`(t=1, -1,

prevprime(t)), nextprime(t)))(10^n):

seq(a(n), n=0..80); # Alois P. Heinz, Aug 13 2014

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_Rick L. Shepherd (rshepherd2(AT)hotmail.com), _, Mar 02 2006

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Integer k such that 10^n + k = A115062(n).

1, 1, 1, -3, 7, 3, 3, -9, 7, 7, 19, 3, -11, -29, -27, -11, 61, -3, 3, -39, -11, -101, 9, -23, 7, 13, 67, -99, -209, -27, -11, -27, -21, -9, 193, -23, 67, 43, -59, 3, -17, 109, 63, 57, 31, -9, -33, 33, -33, 9, -57, 121, -231, 171, 31, 21, 3, -93, -149, 19, 7, -39, -83, 121, -51, 49, 49, 49, 99, 9, 33, -53, 39, 79, -47, 129, 133

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For terms after the first several, 10^n + a(n) is only known to be a highly probable prime. If, for m>0, 10^n - m and 10^n + m are both nearest primes to 10^n, a(n) = -m. For example, a(17) = -3 as 10^17-3 and 10^17+3 are the nearest primes to 10^17. Similarly, a(45) = -9 with both 10^45-9 and 10^45+9 prime.

a(n) = A115062(n) - 10^n.

a(4) = 7 as 10^4 + 7 = 10007 = A115062(4), the nearest prime to 10^4.

Cf. A115062.

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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Mar 02 2006

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