A286094 Nonprime numbers k such that k^4 + k^3 + k^2 + k + 1 is prime.

1, 12, 22, 24, 28, 30, 40, 44, 50, 62, 63, 68, 74, 77, 85, 94, 99, 110, 117, 118, 120, 122, 129, 134, 143, 145, 154, 162, 164, 165, 172, 175, 177, 198, 204, 208, 222, 249, 254, 255, 260, 265, 274, 275, 285, 288, 292, 304, 308, 327, 340, 352, 369, 393, 408, 414

Offset

1,2

Comments

A065509 Union {this sequence} = A049409.

The corresponding prime numbers k^4 + k^3 + k^2 + k + 1 = 11111_k are in A193366; these Brazilian primes, except 5 which is not Brazilian, belong to A085104 and A285017.

Links

R. J. Cano, Table of n, a(n) for n = 1..10000

Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38.

Example

12 is in the sequence because 12^4 + 12^3 + 12^2 + 12 + 1 = 11111_12 = 22621, which is prime.

Mathematica

Select[Range@ 414, And[! PrimeQ@ #, PrimeQ[Total[#^Range[0, 4]]]] &] (* Michael De Vlieger, May 03 2017 *)

Prog

(PARI) isok(n)=if(n==1, 5, if(ispseudoprime(n), 0, isprime(fromdigits([1, 1, 1, 1, 1], n))));
getfirstterms(n)={my(L:list, c:small); L=List(); c=0; forstep(k=1, +oo, 1, if(isok(k), listput(L, k); if(c++==n, break))); return(Vec(L))} \\ R. J. Cano, May 09 2017

Crossrefs

Cf. A049409, A065509, A085104, A088548, A125134, A190527, A193366, A285017.

Sequence in context: A031186 A078538 A278030 * A348187 A098955 A285470

Adjacent sequences: A286091 A286092 A286093 * A286095 A286096 A286097

Keyword

nonn

Author

Bernard Schott, May 02 2017

Status

approved