A293907 Numbers n for which 10^n mod n = 2^k for some positive integer k.
6, 12, 14, 24, 28, 34, 46, 48, 52, 56, 68, 72, 84, 92, 96, 112, 117, 123, 126, 136, 144, 168, 186, 192, 204, 208, 224, 228, 249, 252, 266, 272, 288, 328, 336, 356, 372, 384, 392, 408, 416, 448, 464, 488, 498, 504, 516
Offset: 1
Keywords
Examples
For n = 6, 10^6 mod 6 = 4 = 2^2; For n = 14, 10^14 mod 14 = 2 = 2^1; For n = 84, 10^84 mod 84 = 64 = 2^6; For n = 272, 10^272 mod 272 = 256 = 2^8.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A056969 (10^n modulo n).
Programs
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Mathematica
pm2Q[n_]:=Module[{c=PowerMod[10,n,n]},c>1&&IntegerQ[Log2[c]]]; Select[ Range[600],pm2Q] (* Harvey P. Dale, Mar 29 2023 *) -
PARI
is(n)=my(k=lift(Mod(10,n)^n)); k>1 && k>>valuation(k,2)==1 \\ Charles R Greathouse IV, Oct 19 2017
Extensions
More terms from Michel Marcus, Oct 19 2017
Comments