cp's OEIS Frontend

A103548 a(n) is the largest n-digit zeroless prime such that the sum of the two numbers that result from splitting a(n) between any two of its digits is a distinct prime.

%I A103548 #15 Aug 28 2023 12:15:36
%S A103548 89,863,8821,68683,864883,6866683
%N A103548 a(n) is the largest n-digit zeroless prime such that the sum of the two numbers that result from splitting a(n) between any two of its digits is a distinct prime.
%C A103548 There is no such 8-digit prime, i.e., the sequence ends at a(7) -- although in theory a(n) might exist for some n > 8. - _Hagen von Eitzen_, Jun 02 2009
%C A103548 A term must have the last digit coprime to 10 (odd and not divisible by 5), the others from {2, 4, 6, 8}. - _David A. Corneth_, Aug 28 2023
%e A103548 a(4) = 8821:
%e A103548   8 + 821 = 829, which is prime;
%e A103548   88 + 21 = 109, which is prime;
%e A103548   882 + 1 = 883, which is prime;
%e A103548 and no larger 4-digit number has this property.
%o A103548 (PARI) a(n) = {my(lds = [9,7,3,1], s = (10^n\9-1)*10); forvec(x = vector(n-1,i,[1,4]), b = s - 20*fromdigits(Vec(x)); for(j = 1, #lds, if(iscan(b + lds[j]), return(b + lds[j])))); -1}
%o A103548 (PARI) iscan(n) = {if(n%3 == 0, return(0)); if(!isprime(n), return(0)); my(l = List(), lp, rp, qd = #digits(n-1)); for(i = 1, qd, rp = n % 10^i; lp = n \ 10^i; if(!isprime(rp + lp), return(0), listput(l, rp + lp))); #Set(l) == qd} \\ _David A. Corneth_, Aug 28 2023
%Y A103548 Cf. A038618.
%K A103548 base,fini,full,nonn
%O A103548 2,1
%A A103548 _Ray G. Opao_, Mar 23 2005
%E A103548 Last terms a(6) and a(7) from _Hagen von Eitzen_, Jun 02 2009