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A067860 Primes which are the concatenation of numbers n_1, n_2, n_3, in that order, with n_1 + n_2 = n_3 (leading zeros are forbidden for nonzero n_i).

%I A067860 #24 Mar 08 2025 14:54:33
%S A067860 101,167,257,347,617,5813,7411,8311,8513,9413,9817,10111,10313,11213,
%T A067860 11617,12113,12517,12829,13417,13619,14243,14519,14923,15217,15823,
%U A067860 15859,16061,16319,17623,18119,18523,19423,19697,20323,20929,21517,22123,23537,23629,23831,24547
%N A067860 Primes which are the concatenation of numbers n_1, n_2, n_3, in that order, with n_1 + n_2 = n_3 (leading zeros are forbidden for nonzero n_i).
%H A067860 David A. Corneth, <a href="/A067860/b067860.txt">Table of n, a(n) for n = 1..10000</a>
%H A067860 David A. Corneth, <a href="/A067860/a067860.gp.txt">PARI program</a>
%e A067860 167 is the concatenation of 1, 6, 7 and 1+6 = 7.
%o A067860 (PARI) is(n)=if(n==101, return(1)); my(d=digits(n)); for(i=1,#d-2, for(j=i+1,#d-1, if(digits(fromdigits(d[1..i])+fromdigits(d[i+1..j]))==d[j+1..#d] && (d[i+1] || i==j+1), return(isprime(n))))); 0
%o A067860 select(is,primes(10^4)) \\ _Charles R Greathouse IV_, Sep 21 2015
%o A067860 (PARI) \\ See PARI link. _David A. Corneth_, Mar 06 2021
%Y A067860 See A088291 for another version.
%K A067860 base,nonn
%O A067860 1,1
%A A067860 _Joseph L. Pe_, Feb 15 2002
%E A067860 More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002
%E A067860 Data corrected and more terms from _David A. Corneth_, Mar 06 2021