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

1,2

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.

Links

Table of n, a(n) for n=1..70.

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A247424 A305635 A334420 * A357014 A056911 A152955

Adjacent sequences: A342141 A342142 A342143 * A342145 A342146 A342147

Keyword

nonn

Author

Owen C. Keith, Mar 01 2021

Status

approved