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A260989 Integers n such that prime(n-1) + prime(n+1) is a multiple of n.

%I A260989 #23 Sep 08 2022 08:46:13
%S A260989 4,5,8,11,12,18,20,70,72,1053,4116,6459,6460,40083,63328,251742,
%T A260989 399924,637320,637322,637330,2582288,2582436,2582488,10553828,
%U A260989 16899042,69709721,179992913,179992922,465769813,749973302,749973314,1208198617,1208198629
%N A260989 Integers n such that prime(n-1) + prime(n+1) is a multiple of n.
%H A260989 Zak Seidov, <a href="/A260989/a260989.txt">Table of n, (c=prime(n-1)+prime(n-1), c/n</a>
%e A260989 n=4: prime(n-1) + prime(n+1) = 5 + 11 = 16 = 4*n,
%e A260989 n=20: 67 + 73 = 140 = 7*n,
%e A260989 n=16899042: 312632263 + 312632291 = 625264554 = 37*n,
%e A260989 n=69709721: 1394194387 + 1394194453 = 2788388840 = 40*n.
%t A260989 Select[Range[2, 100000], Mod[Prime[# - 1] + Prime[# + 1], #] == 0 &] (* _Michael De Vlieger_, Aug 07 2015 *)
%o A260989 (PARI) a=2;b=5;for(n=2,10^8,c=a+b;if(c%n<1,print1(n", "));a=nextprime(a+1);b=nextprime(b+1))
%o A260989 (PARI) p=2;q=3;n=1; forprime(r=5,1e9, if((p+r)%n++==0, print1(n", "));p=q;q=r) \\ _Charles R Greathouse IV_, Aug 10 2015
%o A260989 (Magma) [n: n in [2..7*10^3], k in [2..7*10^3] | (NthPrime(n-1) + NthPrime(n+1)) eq n*k]; // _Vincenzo Librandi_, Aug 07 2015
%Y A260989 Cf. A000040, A004648, A048448, A045924, A023143, A092044, A092045, A156149.
%K A260989 nonn
%O A260989 1,1
%A A260989 _Zak Seidov_, Aug 06 2015
%E A260989 a(27)-a(33) from _Charles R Greathouse IV_, Aug 10 2015