A173700 a(n+1) is the smallest integer > a(n) such that the concatenation of a(n), [a(n+1)-a(n)] and a(n+1) is a prime number.

1, 7, 11, 13, 17, 23, 29, 31, 41, 43, 49, 59, 71, 79, 91, 1019, 1033, 1073, 1087, 1091, 1093, 1127, 1139, 1163, 1169, 1187, 1193, 1219, 1223, 1237, 1243, 1259, 1301, 1307, 1337, 1339, 1349, 1373, 1403, 1433, 1483, 1489, 1493, 1501, 1547, 1549, 1567, 1577, 1579, 1601, 1631, 1633, 1657, 1661, 1673, 1679, 11683, 11789, 11903, 11911

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Example

The second term is 7 because 167 is prime [concatenation of 1, the difference (7-1) and 7]. The third term is 11 because 7411 is prime [concatenation of 7, the difference (11-7) and 11]. The next term is 13 because 11213 is prime [concatenation of 11, the difference (13-11) and 13]. And so on. The next term is always the smallest available.

Maple

S3:= proc(n) option remember; local a, d;
       if n=1 then 1
     else a:= S3(n-1);
          for d while not isprime(parse(cat(a, d, a+d)))
          do od; a+d
       fi
     end:
seq(S3(n), n=1..60);

Mathematica

nxt[a_]:=Module[{k=a+2}, While[CompositeQ[FromDigits[Join[ IntegerDigits[ a], IntegerDigits[k-a], IntegerDigits[k]]]], k+=2]; k]; NestList[nxt, 1, 60] (* Harvey P. Dale, Sep 08 2020 *)

Crossrefs

Sequence in context: A260714 A049481 A175412 * A067557 A103485 A191079

Adjacent sequences: A173697 A173698 A173699 * A173701 A173702 A173703

Keyword

nonn,base

Author

Alois P. Heinz and Eric Angelini, Nov 25 2010

Status

approved