A342144 Numbers m with integer solution to x^x == (x+1)^(x+1) (mod m) with x > 0.

1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 119, 123, 127, 129, 131, 133, 137, 139, 141, 143, 145, 147, 149, 151, 155, 157, 159, 161, 163, 167

Offset: 1

Author

Owen C. Keith, Mar 01 2021

Keywords

• nonn

Comments

Some values of m have multiple solutions.

For example, for m = 49, 25^25 == 26^26 (mod 49) and 37^37 == 38^38 (mod 49).

All terms are odd.

First differs from A334420 at a(70) which is 167 for this sequence and 165 for A334420.

First differs from A056911 at a(21) which is 49 for this sequence and 51 for A056911.

Examples

			3 is a term since 1^1 == 2^2 (mod 3).
5 is a term since 11^11 == 12^12 (mod 5).
		

Crossrefs

Cf. A056911, A084820, A174824, A334420, A338445.

Programs

Mathematica

seqQ[n_] := AnyTrue[Range[LCM[n, CarmichaelLambda[n]]+1], PowerMod[#, #, n] == PowerMod[# + 1, # + 1, n] &]; Select[Range[145], seqQ]