A277401 Positive integers n such that 7^n == 2 (mod n).

1, 5, 143, 1133, 2171, 8567, 16805, 208091, 1887043, 517295383, 878436591673

Offset

1,2

Comments

All terms are odd.

No other terms below 10^15. Some larger terms: 181204957971619289, 21305718571846184078167, 157*(7^157-2)/1355 (132 digits). - Max Alekseyev, Oct 18 2016

Links

Table of n, a(n) for n=1..11.

Formula

A066438(a(n)) = 2 for n > 1.

Example

7 == 2 mod 1, so 1 is a term;
16807 == 2 mod 5, so 5 is a term.

Mathematica

Join[{1}, Select[Range[5173*10^5], PowerMod[7, #, #]==2&]] (* The program will generate the first 10 terms of the sequence; it would take a very long time to generate the 11th term. *) (* Harvey P. Dale, Apr 15 2020 *)

Prog

(PARI) isok(n) = Mod(7, n)^n == 2; \\ Michel Marcus, Oct 13 2016

Crossrefs

Cf. A066438.

Cf. Solutions to 7^n == k (mod n): A277371 (k=-3), A277370 (k=-2), A015954 (k=-1), A067947 (k=1), this sequence (k=2), A277554 (k=3).

Cf. Solutions to b^n == 2 (mod n): A015919 (b=2), A276671 (b=3), A130421 (b=4), A124246 (b=5), this sequence (b=7), A116622 (b=13).

Sequence in context: A006269 A066264 A171776 * A208874 A222289 A134503

Adjacent sequences: A277398 A277399 A277400 * A277402 A277403 A277404

Keyword

nonn,more

Author

Seiichi Manyama, Oct 13 2016

Extensions

a(10) from Michel Marcus, Oct 13 2016

a(11) from Max Alekseyev, Oct 18 2016

Status

approved