A081318 Integers n such that the reciprocal of the largest prime factor of 10^n-1 is not a repeating decimal fraction with a period of n.

6, 18, 22, 30, 32, 38, 42, 46, 54, 66, 74, 78, 82, 90, 94, 96, 110, 118, 132, 138, 146, 154, 162, 174, 186, 194, 198, 206, 210, 218, 228, 231, 240, 242, 254, 258, 260, 264, 266, 268, 274, 282, 284, 286, 298, 300, 306, 310, 318, 322, 334, 338, 344, 348

Offset: 1

Author

Hugo Pfoertner, Mar 18 2003

Keywords

• more
• nonn

Comments

For all but three of the terms through a(41)=274, the reciprocal of the largest prime factor of 10^a(n)-1 is a decimal fraction with a period of a(n)/2. Of the three exceptions, there are two (a(32)=231 and a(38)=264) where the period is a(n)/3, and one (a(19)=132) where the period is a(n)/4. - Jon E. Schoenfield, Jun 27 2010

Examples

			30 is in the sequence because the factorization of 10^30-1 is 3^3*7*11*13*31*37*41*211*241*271*2161*9091*2906161 and 2906161 occurs already in 10^15-1=3^3*31*37*41*271*2906161 producing a decimal fraction with a period of 15, (1/2906161=0.000000344096559000000344096559000000344...)
		

Links

• Makoto Kamada, Factorizations of 11...11 (repunit).

Crossrefs

Cf. A081317.

Formula

Integers n such that A061075(n) is not equal to A005422(n).

Extensions

More terms from Hans Havermann, May 31 2003

Terms a(31)-a(37) from Jon E. Schoenfield, Jun 19 2010

Terms a(38)-a(41) added, link added, and earlier comment expanded by Jon E. Schoenfield, Jun 27 2010

a(42)-a(54) from Max Alekseyev, Aug 17 2013, Apr 26 2022