A173698 a(n+1) is the smallest integer > a(n) such that the concatenation of a(n) and [a(n+1)-a(n)] is a prime number.

1, 2, 5, 8, 11, 14, 23, 26, 29, 32, 49, 50, 53, 76, 77, 80, 89, 112, 115, 116, 119, 122, 125, 134, 145, 146, 167, 196, 257, 266, 269, 272, 281, 290, 293, 302, 305, 322, 323, 344, 353, 356, 373, 376, 377, 386, 389, 406, 433, 440, 449, 452, 455, 478, 481, 484, 497, 500, 503, 512

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

The second term is 2 because 11 is prime [concatenation of 1 and the difference (2-1)]. The third term is 5 because 23 is prime [concatenation of 2 and the difference (5-2)]. The next term is 8 because 53 is prime [concatenation of 5 and the difference (8-5)]. And so on. The next term is always the smallest available.

Maple

S1:= proc(n) option remember;
  local a, d;
    if n=1 then 1
  else a:= S1(n-1);
       for d while not isprime(parse(cat(a, d)))
       do od;
       a+d
  fi
end:
seq(S1(n), n=1..60); # Alois P. Heinz, Nov 25 2011

Mathematica

con[n_]:=Module[{k=n+1, idn=IntegerDigits[n]}, While[!PrimeQ[FromDigits[Join[idn, IntegerDigits[ k-n]]]], k++]; k]; NestList[con, 1, 60] (* Harvey P. Dale, May 17 2023 *)

Crossrefs

Sequence in context: A102795 A275603 A275604 * A162938 A356447 A353985

Adjacent sequences: A173695 A173696 A173697 * A173699 A173700 A173701

Keyword

nonn,base

Author

Eric Angelini, Nov 25 2010

Status

approved