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A070157 Numbers k such that k-1, k+1, k^2+1, k^4+1 and k^8+1 are all prime numbers.

%I A070157 #13 Jun 27 2024 01:41:56
%S A070157 4,19380,9443670,11054760,15992070,22482330,32557380,51102510,
%T A070157 57978840,60549240,64671570,84045960,89757960,111316170,112821690,
%U A070157 116433510,171124380,171418650,183082350,196694760,197021160,241803240,266498460
%N A070157 Numbers k such that k-1, k+1, k^2+1, k^4+1 and k^8+1 are all prime numbers.
%H A070157 Amiram Eldar, <a href="/A070157/b070157.txt">Table of n, a(n) for n = 1..1000</a>
%e A070157 19380 is a term since 19380-1 = 19379, 19380+1 = 19381, 19380^2+1 = 375584401, 19380^4+1 = 141063641523360001 and 19380^8+1 = 19898950959831015581425689600000001 are primes.
%t A070157 Do[p = Prime[n] + 1; If[ PrimeQ[p + 1] && PrimeQ[1 + p^2] && PrimeQ[1 + p^4] && PrimeQ[1 + p^8], Print[p]], {n, 1, 115000000}]
%t A070157 Select[Range[2665*10^5],AllTrue[{#-1,#+1,#^2+1,#^4+1,#^8+1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 03 2019 *)
%o A070157 (PARI) is(k) = isprime(k-1) && isprime(k+1) && isprime(k^2+1) && isprime(k^4+1) && isprime(k^8+1); \\ _Amiram Eldar_, Jun 26 2024
%Y A070157 Subsequence of A070155 and A070156.
%K A070157 nonn
%O A070157 1,1
%A A070157 _Labos Elemer_, Apr 23 2002
%E A070157 Edited and extended by _Robert G. Wilson v_, May 04 2002