A104179 Primes that are either single-digit primes or a concatenation of two earlier terms.
2, 3, 5, 7, 23, 37, 53, 73, 223, 233, 337, 353, 373, 523, 733, 773, 2237, 2333, 3373, 3533, 3733, 5233, 5237, 5323, 7333, 7523, 23333, 23773, 25237, 32237, 33533, 33773, 35323, 35353, 37223, 37337, 52237, 53233, 53353, 53773, 73523, 75323, 77323
Offset: 1
Links
- Karl W. Heuer, Table of n, a(n) for n = 1..13849 (first 1003 terms from Jean-Marc Falcoz)
Crossrefs
Programs
-
PARI
isDW(p,i=1)={while(p>i*=10,setminus(Set(divrem(p,i)),a)||return(eval(Set(Vec(Str(p)))[1])));p<9} a=[]; forprime( p=2, 99999, isDW(p) & !print1(p",") & a=setunion(a,Set(p))) \\ M. F. Hasler, Mar 28 2009
Formula
Up to 10^12 there are only 1003 terms and the n-th term seems to be roughly n^(10/e). - Jean-Marc Falcoz, Mar 28 2009
Although the n-th term does seem to be O(n^c), a better estimate for c is 4.38 rather than 10/e. The multiplier will be bounded but not convergent -- it jumps by a factor of 20/7 as we cross from a k-digit number beginning 777 to a (k+1)-digit number beginning 2222. - Karl W. Heuer, Sep 23 2024
Extensions
More terms from M. F. Hasler, Mar 28 2009