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

Author

Robert Israel, Nov 04 2015

Keywords

• nonn
• base

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.

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Math StackExchange, Consecutive numbers where their revers numbers are primes

Crossrefs

Cf. A000040, A004086, A049054, A095179.

Programs

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 *)

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