A083756 Beginning with 5, rearrangement of odd primes such that every concatenation beginning with the first term is a prime.

5, 3, 23, 13, 17, 19, 11, 31, 47, 109, 89, 571, 53, 271, 149, 151, 101, 409, 173, 241, 587, 337, 1091, 1303, 251, 457, 431, 373, 947, 1447, 2153, 577, 419, 463, 797, 349, 1019, 1063, 557, 619, 2549, 2113, 3257, 331, 383, 1201, 227, 1033, 2333, 3253, 1061, 7

Offset

1,1

Comments

Conjecture: every odd prime is a member.

Links

Robert Israel, Table of n, a(n) for n = 1..300

Maple

xcat:= proc(a, b) 10^(1+ilog10(b))*a+b end proc:
A[1]:= 5; C:= A[1]:
Cands:= select(isprime, [3, seq(i, i=7..10^6, 2)]):
for n from 2 to 100 do
  found:= false;
  for i from 1 to nops(Cands) while not found do
    x:= Cands[i];
    cx:= xcat(C, x);
    if isprime(cx) then
        found:= true;
        C:= cx;
        Cands:= subsop(i=NULL, Cands);
        A[n]:= x;
    fi
  od;
  if not found then break fi;
od:
seq(A[i], i=1..n-1); # Robert Israel, May 05 2016

Mathematica

L={5}; v=5; While[Length@L < 100, p=3; While[MemberQ[L, p] || CompositeQ[w = v* 10^IntegerLength[p] + p], p = NextPrime[p]]; AppendTo[L, p]; v=w]; L (* Giovanni Resta, May 05 2016 *)

Crossrefs

Cf. A083757.

Sequence in context: A303634 A069607 A128366 * A283507 A290074 A146317

Adjacent sequences: A083753 A083754 A083755 * A083757 A083758 A083759

Keyword

base,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003

Extensions

More terms from Max Alekseyev, Aug 15 2013

Status

approved