A367796 - OEIS

%I #29 Dec 30 2023 23:12:00

%S 2,29,47,83,20147,23117,24107,63113,80141,81131,261104399,262005299,

%T 262104299,262203299,263302199,264203099,264302099,264500099,

%U 270401489,271500389,273104189,273302189,274401089,282203279,284302079,284500079,291104369,291203369,292005269,293005169,293104169,294302069

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

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

%H David A. Corneth, <a href="/A367796/b367796.txt">Table of n, a(n) for n = 1..5743</a> (terms <= 10^15)

%H David A. Corneth, <a href="/A367796/a367796.gp.txt">PARI program</a>

%e A056964(a(n)) = 121 = 11^2 for 2 <= n <= 4.

%e A056964(a(n)) = 94249 = 307^2 for 5 <= n <= 10.

%e A056964(a(n)) = 1254505561 = 35419^2 for 11 <= n <= 71.

%p digrev:= proc(n) local L,i;

%p   L:= convert(n,base,10);

%p   add(L[-i]*10^(i-1),i=1..nops(L))

%p end proc:

%p filter:= proc(t) local v;

%p   v:= sqrt(t+digrev(t));

%p   v::integer and isprime(v)

%p end proc:

%p R:= 2, 29, 47, 83: count:= 4: flag:= true:

%p for d from 3 to 9 by 2 do

%p   p:= prevprime(10^(d-1));

%p   for i from 1 do

%p     p:= nextprime(p);

%p     p1:= floor(p/10^(d-1));

%p     if p1::odd then p:= nextprime((p1+1)*10^(d-1)) fi;

%p     if p > 10^d then break fi;

%p     if filter(p) then

%p        count:= count+1; R:= R,p;

%p fi od od:

%p R;

%t Select[Prime[Range[10^6]], PrimeQ[Sqrt[#+FromDigits[Reverse[IntegerDigits[#]]]]] &] (* _Stefano Spezia_, Dec 10 2023 *)

%o (PARI) \\ See PARI link

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

%K nonn,base

%O 1,1

%A _Robert Israel_, Nov 30 2023