A089394 Largest n-digit member of A089392, or 0 if there is no such n-digit term.

7, 89, 881, 8821, 80849, 864883, 8608081, 48804809, 608844043, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Amarnath Murthy, Nov 10 2003

Keywords

• base
• nonn

Comments

A089392 has no members with 10, 11, or 12 digits. It is unlikely that it has any with more than 12 digits. - David Wasserman, Sep 15 2005

Giovanni Resta has checked this up to 16 digits. Indeed 5391391551358 and 97393713331910 are the only 13- resp. 14-digit numbers (not primes) with this property, i.e., in A252996. See Carlos Rivera's puzzle page for a probabilistic argument concerning the finiteness. - M. F. Hasler, Dec 25 and Dec 28 2014

Links

• C. Rivera, Puzzle 401. Magnanimous primes, 2007.

Crossrefs

Cf. A089392, A089393, A252996, A252495.

Programs

Maple

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 by -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):break fi od od: # C. Ronaldo

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

3 more terms from David Wasserman, Sep 15 2005

Definition edited and a(10..16) = 0 added by M. F. Hasler, Dec 28 2014