A124113 a(n) = largest composite number of n decimal digits that becomes prime by decreasing any one of the higher-order digits.

99, 987, 9951, 99939, 996983, 9981153, 99745289, 981196517, 9927756573, 99243774623, 992617385333, 9751651447377

Offset

2,1

Comments

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

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

Links

Table of n, a(n) for n=2..13.

Example

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

Prog

(PARI) A124113(d)={
    forstep(n=10^d-1, 10^d\9, [-2, -4, -2, -2],
        if(isA124113(n, d), return(n))
    )
};
isA124113(n, d)={
    if(n%3==1, return(0));
    for(i=1, d-1,
        if(!isprime(n-10^i), return(0))
    );
    my(v=eval(Vec(Str(n))));
    for(i=1, #v,
        if(v[i]==0, return(0))
    );
    !isprime(n)
};

Crossrefs

Sequence in context: A177686 A135219 A182672 * A223157 A223155 A308466

Adjacent sequences: A124110 A124111 A124112 * A124114 A124115 A124116

Keyword

hard,nonn,base

Author

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

Extensions

a(2) corrected, a(7) inserted, and a(11)-a(12) added by Charles R Greathouse IV, Nov 15 2010

a(13) added by Charles R Greathouse IV, Nov 17 2010

Status

approved