A257636 Numbers n such that the base 10 reversals of n and n+1 are both prime.

2, 13, 16, 30, 31, 34, 37, 70, 73, 91, 97, 106, 112, 118, 124, 130, 133, 145, 151, 166, 181, 199, 300, 310, 346, 358, 361, 364, 370, 376, 382, 388, 391, 700, 709, 721, 727, 730, 739, 745, 751, 754, 757, 760, 763, 775, 778, 784, 787, 790, 904, 907, 916, 919

Offset

1,1

Comments

n such that n and n+1 are in A095179.

Leading 0's in the reversals are allowed.

Heuristically, the abundance of these numbers should be roughly similar to that of the twin primes. Thus the sequence should be infinite but the sum of the reciprocals should converge.

All terms == 1 (mod 3) except for 2 and 3*10^k where k is in A049054.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Math StackExchange, Consecutive numbers where their revers numbers are primes

Example

13 is in the sequence because both 31 and 41 are prime.

Maple

revdigs:= proc(n) option remember; local x;
   x:= n mod 10;
   x*10^ilog10(n)+revdigs((n-x)/10);
end proc:
for i from 0 to 9 do revdigs(i):= i od:
Rprimes:= select(isprime@revdigs, [$1..10^4]):
Rprimes[select(t -> Rprimes[t+1]-Rprimes[t]=1, [$1..nops(Rprimes)-1])]; # Robert Israel, Nov 04 2015

Mathematica

SequencePosition[Table[If[PrimeQ[IntegerReverse[n]], 1, 0], {n, 1000}], {1, 1}][[;; , 1]] (* Harvey P. Dale, Jan 07 2024 *)

Prog

(PARI) for(n=1, 1e3, if(isprime(eval(concat(Vecrev(Str(n))))) && isprime(eval(concat(Vecrev(Str(n+1))))), print1(n, ", "))) \\ Altug Alkan, Nov 04 2015

Crossrefs

Cf. A000040, A004086, A049054, A095179.

Sequence in context: A318999 A032453 A298295 * A258317 A318911 A065245

Adjacent sequences: A257633 A257634 A257635 * A257637 A257638 A257639

Keyword

nonn,base

Author

Robert Israel, Nov 04 2015

Status

approved