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%I #24 Sep 08 2022 08:44:49
%S 1,7,11,25,35,43,45,47,51,53,57,63,65,81,91,103,113,117,121,143,149,
%T 169,173,191,193,199,201,211,213,225,235,247,253,255,263,269,299,331,
%U 333,355,357,359,373,385,387,395,399,403,411,445,453,495,519,537,579,599
%N Numbers k such that k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 is prime.
%C Numbers k such that A027622(k) is prime.
%H P. De Geest, <a href="http://www.worldofnumbers.com/sumpower.htm">Palindromic Quasi_Under_Squares of the form n+(n+1)^2</a>
%e k=1: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 3413 = A027886(1),
%e k=7: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 171851 = A027886(2),
%e k=11: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 800143 = A027886(3).
%t With[{c=Total[Table[(#+i)^(i+1),{i,0,4}]]},Select[Range[600],PrimeQ[c]&]] (* _Harvey P. Dale_, May 07 2012 *)
%o (Magma) [n: n in [0..1000] |IsPrime(n+(n+1)^2+(n+2)^3+(n+3)^4+(n+4)^5)] // _Vincenzo Librandi_, Nov 20 2010
%o (PARI) is(n)=isprime(n+(n+1)^2+(n+2)^3+(n+3)^4+(n+4)^5) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A027622, A027886.
%K nonn,easy
%O 1,2
%A _Patrick De Geest_
%E Edited by _N. J. A. Sloane_, May 21 2008 at the suggestion of _R. J. Mathar_
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