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%I #21 Jun 27 2024 22:15:35
%S 1,8,18,21,39,40,51,55,67,85,86,87,123,175,179,185,199,200,216,227,
%T 247,248,260,292,314,351,360,361,407,413,434,441,445,465,479,494,514,
%U 515,565,573,576,580,583,622,629,670,679,684,691,698,712,717,724,734
%N Numbers k such that prime(2k) mod prime(k) = prime(2k+2) mod prime(k+1).
%F prime(2*a(n)) mod prime(a(n)) = prime(2*a(n)+2) mod prime(a(n)+1).
%e a(2)=8 because prime(2*8) mod prime(8) = prime(2*8+2) mod prime(8+1) = 15.
%p A178180:=n->`if`((ithprime(2*n) mod ithprime(n)) = (ithprime(2*n+2) mod ithprime(n+1)),n,NULL): seq(A178180(n), n=1..10^3); # _Wesley Ivan Hurt_, Sep 14 2014
%t Select[Range[800],Mod[Prime[2#],Prime[#]]==Mod[Prime[2#+2],Prime[#+1]]&] (* _Harvey P. Dale_, May 28 2019 *)
%o (PARI) s=[]; for(n=1, 1000, if(prime(2*n)%prime(n) == prime(2*n+2)%prime(n+1), s=concat(s, n))); s \\ _Colin Barker_, Jun 27 2014
%Y Cf. A000040.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Dec 22 2010
%E Corrected by _R. J. Mathar_, Dec 22 2010
%E More terms from _Colin Barker_, Jun 27 2014