cp's OEIS Frontend

A117190 Integer k such that 10^n + k = A115062(n).

%I A117190 #5 Aug 13 2014 22:57:43
%S A117190 1,1,1,-3,7,3,3,-9,7,7,19,3,-11,-29,-27,-11,61,-3,3,-39,-11,-101,9,
%T A117190 -23,7,13,67,-99,-209,-27,-11,-27,-21,-9,193,-23,67,43,-59,3,-17,109,
%U A117190 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
%N A117190 Integer k such that 10^n + k = A115062(n).
%C A117190 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.
%F A117190 a(n) = A115062(n) - 10^n.
%e A117190 a(4) = 7 as 10^4 + 7 = 10007 = A115062(4), the nearest prime to 10^4.
%p A117190 a:= n-> (t->((p, q)->`if`(q-t<t-p, q, p)-t)(`if`(t=1, -1,
%p A117190         prevprime(t)), nextprime(t)))(10^n):
%p A117190 seq(a(n), n=0..80);  # _Alois P. Heinz_, Aug 13 2014
%Y A117190 Cf. A115062.
%K A117190 sign
%O A117190 0,4
%A A117190 _Rick L. Shepherd_, Mar 02 2006