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A372082
Primes p such that the 10's complement A089186(p) and the concatenations of p and A089186(p) and of A089186(p) and p are all prime.
1
3, 7, 17, 29, 71, 83, 281, 719, 1637, 2309, 3701, 4493, 5507, 6299, 7691, 8363, 9029, 11003, 13163, 17117, 18371, 20807, 31181, 31793, 32693, 32843, 33617, 33893, 34211, 34673, 37277, 38453, 49409, 50591, 61547, 62723, 65327, 65789, 66107, 66383, 67157, 67307, 68207, 68819, 79193, 81629, 82883
OFFSET
1,1
COMMENTS
If p is a term and starts with 1 to 8, then its 10's complement A089186(p) is also a term. This is not the case if p starts with 9, as then A089186(A089186(p)) <> p. For example, 9029 is a term but its 10's complement 971 is not a term.
LINKS
EXAMPLE
a(3) = 17 is a term because 17 is a prime, its 10's complement 83 is a prime, and the concatenations 1783 and 8317 are primes.
MAPLE
filter:= proc(n) local d, c;
if not isprime(n) then return false fi;
d:= 10^(1+ilog10(n)); c:= d-n;
isprime(c) and isprime(c*d+n) and isprime(n*10^(1+ilog10(c))+c)
end proc:
select(filter, [seq(i, i=3..10000, 2)]);
CROSSREFS
Cf. A089186. Subset of A083989.
Sequence in context: A191081 A079779 A083991 * A228567 A123988 A006628
KEYWORD
nonn,base
AUTHOR
Robert Israel, Jul 03 2024
STATUS
approved