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.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A372079 A372080 A372081 * A372083 A372084 A372085

Keyword

nonn,base

Author

Robert Israel, Jul 03 2024

Status

approved