Search: id:A089695
Results 1-1 of 1 results found.

%I A089695
%S A089695 2,3,5,7,11,23,29,41,43,47,61,67,83,89,101,227,229,281,401,443,449,467,
%T A089695 601,607,647,661,683,809,821,863,881,4001,4463,4643,6007,6067,6803,8009
%N A089695 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 A089695 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 A089695 No more terms < 10^8. - David Wasserman (wasserma(AT)spawar.navy.mil), 
               Oct 04 2005
%e A089695 863 is a member 863, 8+63, 86+3, 8+6+3 are all prime.
%p A089695 with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1),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^(d-1) to 10^d-1 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 A089695 Cf. A089696.
%Y A089695 Sequence in context: A129945 A046704 A089392 this_sequence A070027 A156658 
               A118723
%Y A089695 Adjacent sequences: A089692 A089693 A089694 this_sequence A089696 A089697 
               A089698
%K A089695 base,nonn
%O A089695 1,1
%A A089695 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 10 2003
%E A089695 Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 
               25 2004

Search completed in 0.001 seconds