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

1,1

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, ....

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

pm2Q[n_]:=Module[{c=PowerMod[10, n, n]}, c>1&&IntegerQ[Log2[c]]]; Select[ Range[600], pm2Q] (* Harvey P. Dale, Mar 29 2023 *)

Prog

(PARI) is(n)=my(k=lift(Mod(10, n)^n)); k>1 && k>>valuation(k, 2)==1 \\ Charles R Greathouse IV, Oct 19 2017

Crossrefs

Cf. A056969 (10^n modulo n).

Sequence in context: A079946 A315614 A118586 * A259397 A183029 A113791

Adjacent sequences: A293904 A293905 A293906 * A293908 A293909 A293910

Keyword

nonn

Author

Björn Ch. Buchli, Oct 19 2017

Extensions

More terms from Michel Marcus, Oct 19 2017

Status

approved