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A194257 Primes of the form p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime. 6

%I #38 Mar 09 2024 12:20:42

%S 127,1093,19531,5229043,25646167,917087137,52379047267,153436090543,

%T 502628805631,11016462577051,18871143464293,251059142817757,

%U 1812169199976451,1940350890330343

%N Primes of the form p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime.

%C These primes are generated by exactly A163268.

%C This sequence is included in A088550.

%C These numbers are repunit primes 1111111_n, so they are Brazilian primes and are terms of A085104.

%C Subsequence of A088550. - _Hartmut F. W. Hoft_, May 05 2017

%H Robert Israel, <a href="/A194257/b194257.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A193574(A163268(n)^6). - _Hartmut F. W. Hoft_, May 08 2017

%p select(isprime, map(p -> add(p^i,i=0..6), select(isprime, [2,seq(i,i=3..1000,2)]))); # _Robert Israel_, May 05 2017

%t a194257[n_] := Select[Map[(Prime[#]^7-1)/(Prime[#]-1)&, Range[n]], PrimeQ]

%t a194257[70] (* data *) (* _Hartmut F. W. Hoft_, May 05 2017 *)

%t Select[Table[Total[p^Range[0,6]],{p,Prime[Range[100]]}],PrimeQ] (* _Harvey P. Dale_, Mar 09 2024 *)

%Y Cf. A085104, A088550, A100330, A163268.

%K nonn

%O 1,1

%A _Bernard Schott_, Dec 21 2012

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)