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

Author

Björn Ch. Buchli, Oct 19 2017

Keywords

• nonn

Comments

Odd numbers in this sequence: 117, 123, 249, 747, 4043, 5031, 11573, 12129, 14481, 29489, 34719, 35549, 84123, 124631, 173329, 217391, 266799, 458523, 472173, 490561, 551759, 658499, 675431, 721773, 800397, 1375569, 1917843, 2300079, 3194787, 3394893, 4236747, 5031039, 5043957, 5169333, ....

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

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