A122490 -id:A122490 - cp's OEIS frontend

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

Amarnath Murthy, Nov 12 2005

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

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

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

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 *)

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

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

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

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

A168159 Distance of the least reversible n-digit prime from 10^(n-1).

Original entry on oeis.org

1, 1, 1, 9, 7, 49, 33, 169, 7, 7, 207, 237, 91, 313, 261, 273, 79, 49, 2901, 51, 441, 193, 9, 531, 289, 1141, 67, 909, 331, 753, 2613, 657, 49, 4459, 603, 1531, 849, 2049, 259, 649, 2119, 1483, 63, 6747, 519, 3133, 937, 1159, 1999, 6921, 2949, 613, 4137, 1977, 31

Offset: 1

M. F. Hasler, Nov 21 2009

A (much) more compact form of A114018 (cf. formula). Since this sequence and A114018 refer to "reversible primes" (A007500), while A122490 seems to use "emirps" (A006567), a(n+1) differs from A122490(n) iff 10^n+1 is prime <=> a(n+1)=1 <=> A114018(n)=10^n+1.

Michael S. Branicky, Table of n, a(n) for n = 1..500

Table[p = NextPrime[y = 10^(n - 1)]; While[! PrimeQ[FromDigits[Reverse[IntegerDigits[p]]]], p = NextPrime[p]]; p - y, {n, 55}] (* Jayanta Basu, Aug 09 2013 *)

for(x=1,1e99, until( isprime(x=nextprime(x+1)) & isprime(eval(concat(vecextract(Vec(Str(x)),"-1..1")))),);print1(x-10^ (#Str(x)-1),", "); x=10^#Str(x)-1)

from sympy import isprime
def c(n): return isprime(n) and isprime(int(str(n)[::-1]))
def a(n): return next(p-10**(n-1) for p in range(10**(n-1), 10**n) if c(p))
print([a(n) for n in range(1, 56)]) # Michael S. Branicky, Jun 27 2022

a(n)=A114018(n)-10^(n-1)

cp's OEIS Frontend

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

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