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

Author

David W. Wilson, Mar 27 2009

Keywords

• nonn
• base

Links

• Karl W. Heuer, Table of n, a(n) for n = 1..13849 (first 1003 terms from Jean-Marc Falcoz)

Crossrefs

Cf. A376433 (number of n-digit terms), A376434 (smallest n-digit term), A376435 (largest n-digit term).

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