A381256 -id:A381256 - cp's OEIS frontend

A381257 Numbers k such that 6*k+1 divides 6^k+1.

0, 1, 6, 30, 58, 70, 73, 90, 101, 105, 121, 125, 146, 153, 166, 170, 181, 182, 185, 210, 233, 241, 242, 266, 282, 290, 322, 373, 381, 385, 390, 397, 441, 445, 446, 450, 453, 530, 557, 562, 585, 593, 601, 602, 605, 606, 621, 646, 653, 670, 685, 710, 726, 805, 810, 817, 833, 837, 853, 866

Offset: 1

René-Louis Clerc, Feb 18 2025

nonn

The numbers are called Curzon numbers by Tattersall (p. 85, exercise 43).

			6*30+1 = 181 divides 6^30+1 = 221073919720733357899777.

James J. Tattersall, Elementary Number Theory in Nine Chapters, Second Edition, Cambridge University Press, 2005, p. 85.

Giovanni Resta,Curzon numbers , Numbers Aplenty.

Cf. A224486, A222948, A230076, A381256, A381258.

Select[Range[0, 866], PowerMod[6, #, 6#+1]==6#&]  (* James C. McMahon, Apr 02 2025 *)

PARI
```
isok(n) = my(m=6*n+1); Mod(6, m)^n==-1
```

A381258 Numbers k such that 7*k+1 divides 7^k+1.

Original entry on oeis.org

0, 1, 135, 5733, 11229, 42705, 50445, 117649, 131365, 168093, 636405, 699825, 1269495, 2528155, 4226175, 6176709, 6502545, 9365265, 9551115, 13227021, 14464485, 14912625, 20859435, 26903605, 28251265, 30589905, 32660901, 37597329, 41506875, 42766465, 55452075, 56192535, 111898605

Offset: 1

René-Louis Clerc, Feb 18 2025

nonn

The numbers are called Curzon numbers by Tattersall (p. 85, exercise 43).

James J. Tattersall, Elementary Number Theory in Nine Chapters, Second Edition, Cambridge University Press, 2005, p. 85.

Giovanni Resta, Curzon numbers, Numbers Aplenty.

Cf. A224486, A222948, A230076, A381256, A381257.

Select[Range[0,10^7],PowerMod[7,#,7#+1]==7#&] (* James C. McMahon, Mar 05 2025 *)

PARI
```
isok(n) = my(m=7*n+1); Mod(7, m)^n==-1
```

cp's OEIS Frontend

A381257 Numbers k such that 6*k+1 divides 6^k+1.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI