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A173446
((n+{0,1})-th prime-1)^2+1 are both primes.
2
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
1,2
COMMENTS
Numbers n such that ((n+{0,1})-th prime-1)^2+1 are both primes.
LINKS
EXAMPLE
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
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
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
126 removed. Terms beyond 247 added by R. J. Mathar, Mar 01 2010
STATUS
approved