A173699 a(n+1) is the smallest integer > a(n) such that the concatenation of [a(n+1)-a(n)] and a(n+1) is a prime number.

1, 3, 7, 9, 11, 17, 21, 23, 33, 47, 53, 57, 61, 63, 67, 69, 71, 77, 83, 87, 91, 93, 101, 111, 113, 131, 141, 143, 1007, 1011, 1013, 1017, 1019, 1023, 1031, 1047, 1051, 1057, 1059, 1061, 1083, 1127, 1131, 1141, 1143, 1157, 1161, 1163, 1169, 1181, 1199, 1203, 1229, 1233, 10027, 10039, 10051, 10053, 10097, 10131

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..140

Example

The second term is 3 because 23 is prime [concatenation of  the difference (3-1) and 3]. The third term is 7 because 47 is prime [concatenation of the difference (7-3) and 7]. The next term is 9 because 29 is prime [concatenation of the difference (9-7) and 9]. And so on. The next term is always the smallest available.

Maple

S2:= proc(n) option remember; local a, d;
       if n=1 then 1
     else a:= S2(n-1);
          for d while not isprime(parse(cat(d, a+d)))
          do od; a+d
       fi
     end:
seq(S2(n), n=1..60);

Mathematica

nxt[n_]:=Module[{k=n+2}, While[!PrimeQ[(k-n)*10^IntegerLength[k]+k], k+=2]; k]; NestList[nxt, 1, 60] (* Harvey P. Dale, Jun 30 2025 *)

Crossrefs

Sequence in context: A256465 A275386 A275602 * A287202 A156770 A088630

Adjacent sequences: A173696 A173697 A173698 * A173700 A173701 A173702

Keyword

nonn,base

Author

Alois P. Heinz and Eric Angelini, Nov 25 2010

Status

approved