A271631 a(1)=1; thereafter each term is the concatenation of consecutive numbers, without repetition, and is coprime to all earlier terms.

1, 2, 3, 4567, 89, 10111213, 1415, 16171819, 2021, 22232425262728293031, 3233, 34353637, 3839, 40414243, 4445464748495051, 52535455565758596061, 6263, 64656667, 6869, 70717273747576777879, 8081, 82838485868788899091, 9293, 949596979899100101102103, 104105106107

Offset

1,2

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

a(2) = 2 because 2 is coprime to 1, a(3) = 3 because 3, 2, 1 are coprime; a(4) cannot be 4 because 2 and 4 have 2 as great common divisor, but cannot be concat(4,5) = 45 because 45 and 3 have 3 as greatest common divisor, neither concat(4,5,6) = 456 because prime factors of 456 are 2, 3 and 19. So a(4) = concat(4,5,6,7) = 4567, a prime.

Maple

P:=proc(q) local a, b, k, n, ok; a:=[1]; print(1); b:=0;
for n from 2 to q do ok:=1; b:=b*10^(ilog10(n)+1)+n; for k from 1 to
nops(a) do if gcd(a[k], b)>1 then ok:=0; break; fi; od;
if ok=1 then print(b); a:=[op(a), b]; b:=0; fi;
od; print(); end: P(10^5);

Mathematica

L={1}; n=1; While[Length@L < 100, t = ++n; While[{1} != Union@ GCD[t, L], n++; t = t*10^IntegerLength[n] + n]; AppendTo[L, t]]; L (* Giovanni Resta, Apr 18 2016 *)

Crossrefs

Cf. A007908.

Sequence in context: A341715 A085943 A068661 * A068826 A085944 A137078

Adjacent sequences: A271628 A271629 A271630 * A271632 A271633 A271634

Keyword

nonn,base,easy

Author

Paolo P. Lava, Apr 18 2016

Status

approved