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

1,1

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)

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A062397 A158578 A003617 * A089770 A249447 A199302

Adjacent sequences: A114015 A114016 A114017 * A114019 A114020 A114021

Keyword

base,nonn

Author

Amarnath Murthy, Nov 12 2005

Extensions

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

Status

approved