A117190 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

Offset

0,4

Comments

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.

Links

Table of n, a(n) for n=0..76.

Formula

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

Example

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

Maple

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

Crossrefs

Cf. A115062.

Sequence in context: A242461 A065443 A198350 * A113584 A111383 A195769

Adjacent sequences: A117187 A117188 A117189 * A117191 A117192 A117193

Keyword

sign

Author

Rick L. Shepherd, Mar 02 2006

Status

approved