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A114018 Least n-digit prime whose digit reversal is also prime. 8
2, 11, 101, 1009, 10007, 100049, 1000033, 10000169, 100000007, 1000000007, 10000000207, 100000000237, 1000000000091, 10000000000313, 100000000000261, 1000000000000273, 10000000000000079, 100000000000000049, 1000000000000002901, 10000000000000000051 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 03:51 EST 2022. Contains 358362 sequences. (Running on oeis4.)