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

1,1

Links

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

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

Prog

(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

Crossrefs

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

Sequence in context: A154385 A125525 A019546 * A096148 A211681 A124674

Adjacent sequences: A104176 A104177 A104178 * A104180 A104181 A104182

Keyword

nonn,base

Author

David W. Wilson, Mar 27 2009

Extensions

More terms from M. F. Hasler, Mar 28 2009

Status

approved