A173071 Palindromic mountain primes.

131, 151, 181, 191, 12421, 12721, 12821, 13831, 13931, 14741, 17971, 1235321, 1245421, 1257521, 1268621, 1278721, 1456541, 1469641, 1489841, 1579751, 1589851, 123484321, 123494321, 123575321, 136797631, 167898761, 12345854321

Offset

1,1

Comments

All terms have an odd number of digits. - Emeric Deutsch, Mar 09 2010

Links

Chai Wah Wu, Table of n, a(n) for n = 1..39

Example

a(6) = 12721; is a palindromic mountain prime.
. . . . .
. . . . .
. . 7 . .
. . . . .
. . . . .
. . . . .
. . . . .
. 2 . 2 .
1 . . . 1

Maple

a := proc (n) local rev, n1: rev := proc (n) local nn: nn := convert(n, base, 10): add(nn[j]*10^(nops(nn)-j), j = 1 .. nops(nn)) end proc: n1 := convert(n, base, 10): if n1[1]=1 and isprime(n) = true and rev(n) = n and n1[1] < n1[2] and n1[2] < n1[3] and n1[3] < n1[4] then n else end if end proc: seq(a(n), n = 1000000 .. 9999999); # this program works only for 7-digit numbers; easily adjustable for other (2k+1)-digit numbers # Emeric Deutsch, Mar 09 2010

Prog

(Python)
from itertools import combinations
from gmpy2 import is_prime
A173071_list = []
for l in range(1, 10):
    for i in combinations('23456789', l):
        s = '1'+''.join(i)
        p = int(s+s[l-1::-1])
        if is_prime(p):
            A173071_list.append(p) # Chai Wah Wu, Nov 05 2015

Crossrefs

Cf. A002113, A002385, A134810, A134811, A134941, A134951.

Sequence in context: A167845 A273049 A134951 * A164294 A155924 A270237

Adjacent sequences: A173068 A173069 A173070 * A173072 A173073 A173074

Keyword

nonn,base,fini,full

Author

Omar E. Pol, Feb 09 2010

Extensions

More terms from Emeric Deutsch, Mar 09 2010, corrected Mar 19 2010

a(22)-a(27) from Donovan Johnson, Jul 22 2010

Status

approved