A376501 Primes that contain at least two different even digits where any permutation of the even digits leaving the odd digits fixed produces a prime. See comments for the treatment of 0.

241, 281, 283, 401, 421, 461, 463, 467, 601, 607, 641, 643, 647, 683, 809, 821, 823, 863, 1021, 1049, 1061, 1069, 1201, 1249, 1283, 1409, 1429, 1487, 1601, 1609, 1823, 1847, 2011, 2027, 2039, 2161, 2207, 2347, 2389, 2411, 2417, 2441, 2459, 2473, 2503, 2543, 2617, 2657, 2671, 2677, 2699, 2707

Offset

1,1

Comments

Primes for which permutations described in the name produce primes with leading 0s are in the sequence but the generated primes with leading 0s are not. For example, a transposition in 401 produces 041, hence 401 is in the sequence but 41 is not.

Links

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

Example

2027, 2207 are primes and 227 is prime with a leading 0 generated by permuting even digits in either 2027 or 2207.  Hence 2027 and 2207 are in the sequence but 227 is not due to the leading 0.
6067, 6607 are primes but 667 generated by permuting even digits in either 6067 or 6607 is not prime, hence by name, neither number is in the sequence.

Maple

filter:= proc(n) local L, oddi, eveni, xodd, i;
 if not isprime(n) then return false fi;
 L:= convert(n, base, 10);
 oddi, eveni:= selectremove(t -> L[t]::odd, [$1..nops(L)]);
 if nops(convert(L[eveni], set))<2 then return false fi;
 xodd:= add(10^(i-1)*L[i], i=oddi);
 andmap(t -> isprime(xodd+add(10^(eveni[i]-1)*L[t[i]], i=1..nops(eveni))), combinat:-permute(eveni))
end proc:
select(filter, [seq(i, i=3..10000, 2)]); # Robert Israel, Oct 23 2024

Crossrefs

Cf. A000040, A003459, A376500, A376502.

Sequence in context: A306151 A075046 A153423 * A050968 A142918 A139502

Adjacent sequences: A376498 A376499 A376500 * A376502 A376503 A376504

Keyword

nonn,base

Author

Enrique Navarrete, Sep 25 2024

Status

approved