%I A089392
%S A089392 2,3,5,7,11,23,29,41,43,47,61,67,83,89,101,227,229,281,401,443,449,467,
%T A089392 601,607,647,661,683,809,821,863,881,2221,2267,2281,2447,4001,4027,4229,
%U A089392 4463,4643,6007,6067,6803,8009,8221,8821,20261,24407,26881,28429,40427
%N A089392 Magnanimous primes: numbers n with following property. Let the digits 
               of n be abcd. Then bcd+a, cd+ab, d+abc, abcd, etc. must all be primes. 
               If n is a k-digit number then it must produce k such primes.
%C A089392 Partition the digits of n by placing a '+' sign any where inside and 
               the result of the expression is prime in every case. Conjecture: 
               Sequence is infinite. 11 is the largest term with all odd digits. 
               2 is the only member with all even digits. In every other term only 
               the least significant digit is odd rest are even by definition. Observation 
               : All two digit primes with the most significant digit even are members.
%e A089392 2267 is a member which gives primes 2+267 = 269, 22+67 = 89, 226+7 = 
               233 and 2267 itself.
%p A089392 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=[[],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 A089392 Cf. A089393, A089394.
%Y A089392 Sequence in context: A078403 A129945 A046704 this_sequence A089695 A070027 
               A156658
%Y A089392 Adjacent sequences: A089389 A089390 A089391 this_sequence A089393 A089394 
               A089395
%K A089392 base,nonn
%O A089392 1,1
%A A089392 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 10 2003
%E A089392 Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 
               25 2004