A306301 Numbers k such that k^2 reversed is a prime and k^2+(k^2 reversed) is a prime.

14, 136, 190, 266, 280, 1036, 1060, 1306, 1406, 1898, 1934, 2660, 2686, 2746, 2776, 3112, 10040, 10250, 10546, 10550, 10630, 10880, 11090, 11156, 11204, 11276, 11354, 11386, 11474, 11740, 11804, 11914, 12064, 12136, 12194, 12250, 12410, 12524, 12626, 12710, 12770, 12794, 12916, 13060

Offset

1,1

Comments

All terms are even and not divisible by 3. - Robert Israel, Apr 09 2019

Links

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

Example

14 is a term because 691 (the reverse of 14^2=196) and 196+691=887 are two prime numbers.

Maple

revdigs:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
filter:= proc(k) local v; v:= revdigs(k^2); isprime(v) and isprime(v+k^2) end proc:
select(filter, [seq(seq(6*i+j, j=[2, 4]), i=0..10000)]); # Robert Israel, Apr 09 2019

Mathematica

Select[Range[50000], PrimeQ[IntegerReverse[#^2]] && PrimeQ[#^2 + IntegerReverse[#^2]] &]

Prog

(PARI) isok(k) = my(kk=fromdigits(Vecrev(digits(k^2)))); isprime(kk) && isprime(k^2+kk); \\ Michel Marcus, Apr 01 2019

Crossrefs

Cf. A007488, A059007, A307046.

Sequence in context: A244651 A004004 A002753 * A155625 A016296 A021044

Adjacent sequences: A306298 A306299 A306300 * A306302 A306303 A306304

Keyword

nonn,base

Author

Robert Price, Mar 31 2019

Status

approved