login
A076611
Palindromic primes with prime middle digit.
1
2, 3, 5, 7, 131, 151, 353, 373, 727, 757, 929, 10301, 10501, 11311, 12721, 13331, 14341, 14741, 15551, 16361, 16561, 19391, 30203, 30703, 31513, 32323, 33533, 34543, 35353, 35753, 36263, 36563, 37273, 37573, 38783, 39293, 70207, 70507
OFFSET
1,1
COMMENTS
There are no such numbers with an even number of digits. This sequence is quite similar to the sequence A071119 up to 12th term.
EXAMPLE
a(12)=10301 is palindromic prime and its middle digit 3 is prime, a(13)=10501 is palindromic prime and its middle digit 5 is prime, a(14)=11311 is palindromic prime and its middle digit 3 is prime, ...
MAPLE
ts_numprapal := proc(n) local ad, adr, midigit; ad := convert(n, base, 10): adr := ListTools[Reverse](ad): if nops(ad) mod 2 = 0 then return 1; fi; midigit := op( (nops(ad)+1)/2, ad ): if (isprime( midigit )='true' and adr=ad) then return 0; else return 1; fi end: ts_pra_num_pal := proc(n) local p1; p1 := ithprime(n): if ts_numprapal(p1) = 0 then return (p1) fi end: apranumpal := [seq(ts_pra_num_pal(i), i=1..100000)]: apranumpal;
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Jani Melik, Oct 21 2002
STATUS
approved