%I
%S 2,3,5,7,11,23,29,41,43,47,61,67,83,89,101,227,229,281,401,443,449,
%T 467,601,607,647,661,683,809,821,863,881,4001,4463,4643,6007,6067,
%U 6803,8009
%N Numbers n such that placing as many possible '+' signs anywhere in between the digits yields a prime in every case. Let abcd... be the digits of n; then abcd, a + bcd, ab + cd, abc + d, a + b + cd, a + bc + d, ab + c + d, a + b + c + d, ... are all prime.
%C Though the first 27 terms match those of A089392, the next term of A089392 (2221) is not a member of this sequence. Conjecture: sequence is finite.
%C No more terms < 10^8.  _David Wasserman_, Oct 04 2005
%e 863 is a member 863, 8 + 63, 86 + 3, 8 + 6 + 3 are all prime.
%p with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j1),j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1,op(i),d+1],i=choose([seq(j,j=2..d)]))]: for n from 10^(d1) to 10^d1 do sn:=convert(n,base,10): fl:=0: for s in sch do m:=add(j,j=[seq(ds(sn[s[i]..s[i+1]1]),i=1..nops(s)1)]): if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ",n) fi od od: # C. Ronaldo
%Y Cf. A089696.
%K base,nonn
%O 1,1
%A _Amarnath Murthy_, Nov 10 2003
%E Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004
