A266675 Do-si-do primes: primes that remain prime when their digits, taken by pairs, are reversed (see comments for more details).

11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 149, 151, 157, 167, 179, 181, 191, 199, 311, 313, 337, 347, 353, 359, 373, 383, 389, 727, 733, 739, 743, 751, 757, 761, 769, 787, 797, 919, 929, 937, 941, 953, 967, 971, 983, 991, 1117, 1171, 1213, 1231, 1297

Offset

1,1

Comments

Primes n with an even number of digits are included if (a) a prime results after reversing n's digits by pairs, e.g., 8971 is a prime and is included because 9817 is also a prime, and (b) n's second digit is not zero. Primes with an odd number of digits are included if (a) a prime results after extracting the middle digit of n, reversing the rest of n's digits by pairs, and inserting the middle digit of n back into the middle of the resulting digits, e.g., 1358471 is a prime and is included because 3148517 is also a prime, and (b) n's second digit is not zero.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

dsdQ[n_/; EvenQ[IntegerLength[n]]]:=Module[{idn=IntegerDigits[n]}, idn[[2]] != 0&&PrimeQ[FromDigits[Flatten[Reverse/@Partition[idn, 2]]]]]; dsdQ[ n_/; OddQ[ IntegerLength[n]]]:=Module[{idn=IntegerDigits[n], len = (IntegerLength[ n]-1)/2, t, fr, ls, md}, t=TakeDrop[idn, len]; fr=t[[1]]; ls=Rest[ t[[2]]]; md=First[t[[2]]]; idn[[2]]!=0&&PrimeQ[FromDigits[ Insert[ Flatten[Reverse/@Partition[Join[fr, ls], 2]], md, len+1]]]]; Select[Prime[Range[5, 500]], dsdQ] (* The program uses the TakeDrop function from Mathematica version 10 *)

Prog

(Perl) use ntheory ":all"; sub is_a266675 { my $n = shift; my @d=todigits($n); return unless is_prime($n) && $d[1] != 0; my $middle = (@d & 1) ? splice(@d, @d>>1, 1) : undef; my @r = @d[map {$_^1} 0..$#d]; splice(@r, @r>>1, 0, $middle) if defined $middle; is_prime(fromdigits(\@r)); } # Dana Jacobsen, Jan 03 2016

Crossrefs

Sequence in context: A111337 A359136 A359137 * A185104 A240570 A354524

Adjacent sequences: A266672 A266673 A266674 * A266676 A266677 A266678

Keyword

nonn,base

Author

Harvey P. Dale, Jan 02 2016

Status

approved