A173446 ((n+{0,1})-th prime-1)^2+1 are both primes.
1, 2, 3, 4, 12, 31, 36, 53, 54, 78, 82, 105, 125, 155, 247, 403, 422, 548, 678, 679, 751, 769, 784, 798, 809, 829, 845, 899, 1049, 1148, 1155, 1312, 1317, 1423, 1436, 1490, 1616, 1688, 1935, 1961, 1990, 1991, 2071, 2181, 2198, 2397, 2437, 2454, 2463, 2556
Offset: 1
Keywords
Examples
a(1)=1 because ((1+0)-th prime-1)^2+1=2=prime and ((1+1)-th prime-1)^2+1=5=prime; a(2)=2 because ((2+0)-th prime-1)^2+1=5=prime and ((2+1)-th prime-1)^2+1=17=prime
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
P:= select(isprime,[2,seq(i,i=3..10^6,2)]): J:= select(i -> isprime((P[i]-1)^2+1),{$1..nops(P)}): sort(convert(J intersect map(`-`,J,1),list)); # Robert Israel, Sep 29 2024
Extensions
126 removed. Terms beyond 247 added by R. J. Mathar, Mar 01 2010
Comments