A089393 Smallest n-digit magnanimous prime (A089392), or 0 if there is no such prime with n digits.

2, 11, 101, 2221, 20261, 220021, 2000221, 20266681, 228440489, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Amarnath Murthy, Nov 10 2003

Keywords

• nonn
• base

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, see Carlos Rivera's puzzle page for a probabilistic argument. - M. F. Hasler, Dec 28 2014

Links

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

Crossrefs

Cf. A089392, A089394, 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 10 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):break fi od od: # C. Ronaldo

Extensions

a(5) and a(6) from Mark Hudson (mrmarkhudson(AT)hotmail.com), Dec 15 2004

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

Two more terms from David Wasserman, Sep 15 2005

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