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

1,1

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

Table of n, a(n) for n=1..16.

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

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

Crossrefs

Cf. A089392, A089394, A252996, A252495.

Sequence in context: A337017 A121419 A099701 * A069664 A130150 A115941

Adjacent sequences: A089390 A089391 A089392 * A089394 A089395 A089396

Keyword

nonn,base

Author

Amarnath Murthy, Nov 10 2003

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

Status

approved