A260989 Integers n such that prime(n-1) + prime(n+1) is a multiple of n.
4, 5, 8, 11, 12, 18, 20, 70, 72, 1053, 4116, 6459, 6460, 40083, 63328, 251742, 399924, 637320, 637322, 637330, 2582288, 2582436, 2582488, 10553828, 16899042, 69709721, 179992913, 179992922, 465769813, 749973302, 749973314, 1208198617, 1208198629
Offset: 1
Keywords
Examples
n=4: prime(n-1) + prime(n+1) = 5 + 11 = 16 = 4*n, n=20: 67 + 73 = 140 = 7*n, n=16899042: 312632263 + 312632291 = 625264554 = 37*n, n=69709721: 1394194387 + 1394194453 = 2788388840 = 40*n.
Links
- Zak Seidov, Table of n, (c=prime(n-1)+prime(n-1), c/n
Programs
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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
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Mathematica
Select[Range[2, 100000], Mod[Prime[# - 1] + Prime[# + 1], #] == 0 &] (* Michael De Vlieger, Aug 07 2015 *)
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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))
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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
Extensions
a(27)-a(33) from Charles R Greathouse IV, Aug 10 2015