A080437 For n < 5, a(n) = n-th prime. For n >= 5, let m = n-th prime. If m is a k-digit prime then a(n) = smallest prime obtained by inserting at least one digit between every pair of digits of m. There are (k-1) places where digit insertion takes place and a(n) contains at least 2k-1 digits.

2, 3, 5, 7, 101, 103, 107, 109, 223, 229, 311, 307, 401, 433, 457, 503, 509, 601, 607, 701, 733, 709, 823, 809, 907, 10061, 10093, 10007, 10009, 10103, 10247, 10301, 10337, 10369, 10429, 10501, 10567, 10613, 10607, 10723, 10709, 10831, 11941

Offset

1,1

Comments

At least up to n = 10^5, one inserted digit per position suffices. - Robert Israel, Feb 12 2016

Links

Matthew M. Conroy and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..168 from Matthew M. Conroy)

Math Overflow, "Can we always attain another prime via inserting digits between the digits of a fixed prime?"

Maple

f:= proc(n) local p, Lp, q0, x, Lx, k, i, q;
  # This function attempts to insert one digit in each position.
  p:= ithprime(n);
  if p < 10 then return p fi;
  Lp:= convert(p, base, 10);
  k:= nops(Lp);
  q0:= add(100^(i-1)*Lp[i], i=1..k);
  for x from 0 to 10^k-1 do
    Lx:= convert(10^k+x, base, 10);
    q:= q0 + 10*add(100^(i-1)*Lx[i], i=1..k-1);
    if isprime(q) then return q fi
  od:
  error("Need more than one digit");
end proc:
map(f, [$1..100]); # Robert Israel, Feb 12 2016

Crossrefs

Cf. A080436.

Sequence in context: A076406 A171050 A092909 * A092908 A050784 A030150

Adjacent sequences: A080434 A080435 A080436 * A080438 A080439 A080440

Keyword

base,nonn

Author

Amarnath Murthy, Feb 21 2003

Extensions

More terms from Matthew Conroy, Sep 18 2007

Status

approved