A114018 Least n-digit prime whose digit reversal is also prime.

2, 11, 101, 1009, 10007, 100049, 1000033, 10000169, 100000007, 1000000007, 10000000207, 100000000237, 1000000000091, 10000000000313, 100000000000261, 1000000000000273, 10000000000000079, 100000000000000049, 1000000000000002901, 10000000000000000051

Offset: 1

Author

Amarnath Murthy, Nov 12 2005

Keywords

• base
• nonn

Comments

The more compact version A168159 gives many more terms, cf. formula. [M. F. Hasler, Nov 21 2009]

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..500 (terms 1..100 from Harvey P. Dale)

Crossrefs

Cf. A168159, A007500, A006567, A122490. [M. F. Hasler, Nov 21 2009]

Programs

Mathematica

f[n_] := Block[{k = 10^(n - 1)}, While[ !PrimeQ[k] || !PrimeQ[FromDigits@Reverse@IntegerDigits@k], k++ ]; k]; Array[f, 19] (* Robert G. Wilson v, Nov 19 2005 *)
lndp[n_]:=Module[{p=NextPrime[10^n]},While[CompositeQ[IntegerReverse[ p]],p = NextPrime[ p]];p]; Array[lndp,20,0] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 05 2019 *)

PARI

for(x=1,1e99, until( isprime(x=nextprime(x+1)) & isprime(eval(concat(vecextract(Vec(Str(x)),"-1..1")))),); print1(x", "); x=10^#Str(x)-1) \\ M. F. Hasler, Nov 21 2009

Python

from sympy import isprime
def c(n): return isprime(n) and isprime(int(str(n)[::-1]))
def a(n): return next(p for p in range(10**(n-1), 10**n) if c(p))
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jun 27 2022

Formula

a(n) = 10^(n-1) + A168159(n). [M. F. Hasler, Nov 21 2009]

Extensions

More terms from Robert G. Wilson v, Nov 19 2005