A124113 - OEIS

%I #13 Apr 29 2021 01:36:32

%S 99,987,9951,99939,996983,9981153,99745289,981196517,9927756573,

%T 99243774623,992617385333,9751651447377

%N a(n) = largest composite number of n decimal digits that becomes prime by decreasing any one of the higher-order digits.

%C a(n) == 0 (mod 7) for n > 6.

%C What is the first n for which a(n) does not exist? Rough heuristics suggest before 20. - _Charles R Greathouse IV_, Nov 18 2010

%e a(5)=99939 is included as 99929, 998939, 98939 and 89939 are primes.

%o (PARI) A124113(d)={

%o     forstep(n=10^d-1,10^d\9,[-2,-4,-2,-2],

%o         if(isA124113(n,d),return(n))

%o     )

%o };

%o isA124113(n,d)={

%o     if(n%3==1,return(0));

%o     for(i=1,d-1,

%o         if(!isprime(n-10^i),return(0))

%o     );

%o     my(v=eval(Vec(Str(n))));

%o     for(i=1,#v,

%o         if(v[i]==0,return(0))

%o     );

%o     !isprime(n)

%o };

%K hard,nonn,base

%O 2,1

%A Anton Vrba (antonvrba(AT)yahoo.com), Nov 29 2006

%E a(2) corrected, a(7) inserted, and a(11)-a(12) added by _Charles R Greathouse IV_, Nov 15 2010

%E a(13) added by _Charles R Greathouse IV_, Nov 17 2010