A277371 Positive integers k that divide 7^k + 3.

1, 2, 4, 5, 26, 205, 2404, 88171, 1785134, 2010899, 58796834, 639723359, 657788549, 2050134685, 4809019972, 6114530474, 11931055777, 1292089439947, 1294667166242, 4586221808305

Offset

1,2

Comments

No other terms below 10^15. Some larger terms: 68363072121992414, 95409505835353571, 1579273736555455916822694118995172, 5481414795965035698701145369881812, 14905708205837180834697194210878924, 45415365018055454586462673640490785681840279, 147329898999183698422689397719859437775766016038732177717811807964. - Max Alekseyev, Oct 18 2016

Links

Table of n, a(n) for n=1..20.

Formula

A066438(a(n)) = a(n) - 3 for n > 2.

Example

7^5 + 3 = 16810 = 5 * 3362, so 5 is a term.

Mathematica

Select[Range[10000], Divisible[7^# + 3, #] &] (* Alonso del Arte, Oct 11 2016 *)
Join[{1, 2}, Select[Range[21*10^5], PowerMod[7, #, #]==#-3&]] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Sep 21 2022 *)

Prog

(PARI) is(n) = Mod(7, n)^n==-3 \\ Felix Fröhlich, Oct 14 2016

Crossrefs

Cf. A066438.

Cf. Solutions to 7^n == k (mod n): this sequence (k=-3), A277370 (k=-2), A015954 (k=-1), A067947 (k=1), A277401 (k=2), A277554 (k=3).

Sequence in context: A163891 A036985 A179133 * A199929 A126666 A036983

Adjacent sequences: A277368 A277369 A277370 * A277372 A277373 A277374

Keyword

nonn,more

Author

Seiichi Manyama, Oct 11 2016

Extensions

a(15)-a(20) from Max Alekseyev, Oct 18 2016

Status

approved