A104179 - OEIS

%I #34 Oct 18 2024 18:13:06

%S 2,3,5,7,23,37,53,73,223,233,337,353,373,523,733,773,2237,2333,3373,

%T 3533,3733,5233,5237,5323,7333,7523,23333,23773,25237,32237,33533,

%U 33773,35323,35353,37223,37337,52237,53233,53353,53773,73523,75323,77323

%N Primes that are either single-digit primes or a concatenation of two earlier terms.

%H Karl W. Heuer, <a href="/A104179/b104179.txt">Table of n, a(n) for n = 1..13849</a> (first 1003 terms from Jean-Marc Falcoz)

%F 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

%F 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

%o (PARI) isDW(p,i=1)={while(p>i*=10,setminus(Set(divrem(p,i)),a)||return(eval(Set(Vec(Str(p)))[1])));p<9}

%o a=[]; forprime( p=2, 99999, isDW(p) & !print1(p",") & a=setunion(a,Set(p))) \\ _M. F. Hasler_, Mar 28 2009

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

%K nonn,base

%O 1,1

%A _David W. Wilson_, Mar 27 2009

%E More terms from _M. F. Hasler_, Mar 28 2009