A308238 Nonprimes k such that k^10 + k^9 + k^8 + k^7 + k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.

1, 20, 21, 30, 60, 86, 172, 195, 212, 224, 258, 268, 272, 319, 339, 355, 365, 366, 390, 398, 414, 480, 504, 534, 539, 543, 567, 592, 626, 654, 735, 756, 766, 770, 778, 806, 812, 874, 943, 973, 1003, 1036, 1040, 1065, 1194, 1210, 1239, 1243, 1264, 1309, 1311

Offset

1,2

Comments

A240693 Union {this sequence} = A162862.

The corresponding prime numbers, (11111111111)_k, are Brazilian primes and belong to A085104 and A285017 (except 11).

Links

Table of n, a(n) for n=1..51.

Example

(11111111111)_20 = (20^11 - 1)/19 = 10778947368421 is prime, thus 20 is a term.

Maple

filter:= n -> not isprime(n) and isprime((n^11-1)/(n-1)) : select(filter, [$2..5000]);

Mathematica

Select[Range@ 1320, And[! PrimeQ@ #, PrimeQ@ Total[#^Range[0, 10]]] &] (* Michael De Vlieger, Jun 09 2019 *)

Prog

(Magma) [1] cat [n:n in [2..1500]|not IsPrime(n) and IsPrime(Floor((n^11-1)/(n-1)))]; // Marius A. Burtea, May 16 2019
(PARI) isok(n) = !isprime(n) && isprime(polcyclo(11, n)); \\ Michel Marcus, May 19 2019

Crossrefs

Cf. A162861, A162862, A240693, A286301.

Intersection of A064108 and A285017.

Similar to A182253 for k^2+k+1, A286094 for k^4+k^3+k^2+k+1, A288939 for k^6+k^5+k^4+k^3+k^2+k+1.

Sequence in context: A295488 A008940 A014368 * A118865 A118608 A176241

Adjacent sequences: A308235 A308236 A308237 * A308239 A308240 A308241

Keyword

nonn

Author

Bernard Schott, May 16 2019

Status

approved