A114017 a(n) = smallest n-digit prime which differs from the previous n-digit prime at every corresponding digit (or 0 if no such prime exists).

3, 23, 211, 2003, 20011, 200003, 3000017, 20000003, 200000033, 2000000011, 20000000089, 300000000077, 2000000000003, 20000000000021, 400000000000063, 2000000000000021, 50000000000000051, 200000000000000003

Offset

1,1

Comments

For n > 1, a(n), if it exists, is of the form nextprime(t*10^(n-1)) for some t, 2 <= t <= 9. [Max Alekseyev, Apr 23 2010]

Links

Table of n, a(n) for n=1..18.

Example

2003 is a term as the previous prime 1999 differs at every corresponding position (1,2), (9,0), (9,0), (9,3).

Mathematica

Table[SelectFirst[Partition[Prime@ Range[PrimePi@ NextPrime[10^n], PrimePi[10^(n + 1) - 1]], 2, 1], AllTrue[Transpose@ {IntegerDigits[#1], IntegerDigits[#2]}, UnsameQ @@ # &] & @@ # &], {n, 0, 7}] [[All, -1]] (* Michael De Vlieger, Aug 14 2017 *)

Prog

(PARI) { a(n) = local(L, U, aa, bb); if(n==1, return(3)); for(t=2, 9, L=precprime(t*10^(n-1)); U=nextprime(t*10^(n-1)); aa=Vec(Str(L)); bb=Vec(Str(U)); if(sum(i=1, #aa, aa[i]!=bb[i])==#aa, return(U)); ); 0 } \\ Max Alekseyev, Apr 23 2010

Crossrefs

Cf. A114016.

Sequence in context: A235131 A235360 A135423 * A316085 A068691 A093135

Adjacent sequences: A114014 A114015 A114016 * A114018 A114019 A114020

Keyword

base,nonn

Author

Amarnath Murthy, Nov 12 2005

Extensions

2 more terms from R. J. Mathar, Aug 31 2007

More terms from Max Alekseyev, Apr 23 2010

Status

approved