cp's OEIS Frontend

A383195 Primes that are the concatenation of three primes, of which two are equal.

%I A383195 #20 Apr 29 2025 13:27:48
%S A383195 223,227,233,277,337,353,373,557,577,727,733,757,773,1733,1777,1933,
%T A383195 2213,2237,2243,2267,2273,2297,2333,2377,3313,3319,3323,3329,3331,
%U A383195 3343,3347,3359,3361,3371,3373,3389,3413,3433,3533,3593,3613,3673,3733,3793,3833,4133,4177,4733,5333,5519,5531,5573
%N A383195 Primes that are the concatenation of three primes, of which two are equal.
%C A383195 Complement of A100633 in A100607.
%H A383195 Robert Israel, <a href="/A383195/b383195.txt">Table of n, a(n) for n = 1..10000</a>
%e A383195 a(3) = 233 is a term because 233 is prime and is the concatenation of the primes 2, 3 and 3, of which two are equal.
%p A383195 filter:= proc(n) local m, i, j, ni, nj, np, n3;
%p A383195  if not isprime(n) then return false fi;
%p A383195  m:= ilog10(n);
%p A383195  for i from 1 to m-1 do
%p A383195    ni:= n mod 10^i;
%p A383195    if ni < 10^(i-1) or not isprime(ni) then next fi;
%p A383195    np:= (n-ni)/10^i;
%p A383195    for j from 1 to m-i do
%p A383195      nj:= np mod 10^j;
%p A383195      if nj < 10^(j-1) then next fi;
%p A383195      n3:= (np-nj)/10^j;
%p A383195      if nops({ni, nj, n3})<3 and isprime(nj) and isprime(n3) then return true fi;
%p A383195  od od;
%p A383195  false
%p A383195 end proc:
%p A383195 select(filter, [seq(i,i=3..10000,2)]);
%Y A383195 Cf. A100607, A100633.
%K A383195 nonn
%O A383195 1,1
%A A383195 _Robert Israel_, Apr 28 2025