A367796 Primes p such that the sum of p and its reversal is the square of a prime.

2, 29, 47, 83, 20147, 23117, 24107, 63113, 80141, 81131, 261104399, 262005299, 262104299, 262203299, 263302199, 264203099, 264302099, 264500099, 270401489, 271500389, 273104189, 273302189, 274401089, 282203279, 284302079, 284500079, 291104369, 291203369, 292005269, 293005169, 293104169, 294302069

Offset: 1

Author

Robert Israel, Nov 30 2023

Keywords

• nonn
• base

Comments

Terms > 83 have an odd number of digits and an even first digit.

Examples

			A056964(a(n)) = 121 = 11^2 for 2 <= n <= 4.
A056964(a(n)) = 94249 = 307^2 for 5 <= n <= 10.
A056964(a(n)) = 1254505561 = 35419^2 for 11 <= n <= 71.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..5743 (terms <= 10^15)
• David A. Corneth, PARI program

Crossrefs

Cf. A056964, A067030, A061783. Subset of A367793.

Programs

Maple

digrev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(t) local v;
  v:= sqrt(t+digrev(t));
  v::integer and isprime(v)
end proc:
R:= 2, 29, 47, 83: count:= 4: flag:= true:
for d from 3 to 9 by 2 do
  p:= prevprime(10^(d-1));
  for i from 1 do
    p:= nextprime(p);
    p1:= floor(p/10^(d-1));
    if p1::odd then p:= nextprime((p1+1)*10^(d-1)) fi;
    if p > 10^d then break fi;
    if filter(p) then
       count:= count+1; R:= R,p;
fi od od:
R;

Mathematica

Select[Prime[Range[10^6]], PrimeQ[Sqrt[#+FromDigits[Reverse[IntegerDigits[#]]]]] &] (* Stefano Spezia, Dec 10 2023 *)

PARI

\\ See PARI link