A090260 Beginning with 1, distinct numbers such that concatenation a(n+1), a(n), a(n+1) is a prime.

1, 3, 11, 13, 17, 7, 111, 23, 9, 19, 27, 43, 33, 29, 31, 41, 37, 21, 53, 51, 47, 39, 73, 107, 49, 59, 57, 61, 71, 63, 79, 77, 67, 87, 97, 81, 89, 103, 69, 109, 93, 113, 99, 1019, 123, 131, 117, 101, 1017, 139, 173, 91, 137, 171, 127, 143, 141, 83, 181, 119, 151, 129, 133

Offset

1,2

Comments

Conjecture: all positive integers coprime to 10 occur in the sequence. - Robert Israel, Jan 14 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

313,11311,131113 etc. are all primes.

Maple

aba:= proc(a, b) (a*10^(1+ilog10(b))+b)*10^(1+ilog10(a))+a end proc:
Cands:= remove(t -> t mod 5 = 0, [seq(i, i=3 .. 10^5, 2)]):
R:= 1: x:= 1: nC:= nops(Cands):
for n from 2 to 100 do
  found:= false:
  for i from 1 to nC do
    if isprime(aba(Cands[i], x)) then
      found:= true;
      R:= R, Cands[i];
      x:= Cands[i];
      Cands:= subsop(i=NULL, Cands);
      nC:= nC-1;
      break
    fi
  od; if not found then break fi;
od:
R; # Robert Israel, Jan 14 2025

Crossrefs

Cf. A090261.

Sequence in context: A177335 A031449 A305859 * A179522 A020635 A175820

Adjacent sequences: A090257 A090258 A090259 * A090261 A090262 A090263

Keyword

base,nonn,look

Author

Amarnath Murthy, Nov 28 2003

Extensions

More terms from David Wasserman, Apr 22 2004

Status

approved