A181362 a(n) is the starting position of the n-th occurrence of n in the string 123456789101112131415161718192021... .

1, 15, 37, 59, 81, 103, 125, 147, 169, 214, 235, 271, 307, 533, 836, 1139, 1442, 1745, 2048, 2651, 541, 708, 978, 1308, 1608, 1908, 2208, 2508, 2808, 4115, 2684, 3020, 3424, 3428, 4232, 4331, 4375, 4419, 4463, 6652, 3229, 4595, 4639, 4679, 4719, 4767

Offset: 1

Author

Jon Palin (jon.palin(AT)gmail.com), Oct 15 2010

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..2000
• Project Euler, Problem 305: Reflexive Position

Crossrefs

Cf. A033307, A031297 (first occurrence).

Programs

Maple

M:= 10000: S:= cat(seq(i,i=1..M)):
f:= proc(n) local i,R; global S, M;
   R:= [StringTools:-SearchAll(sprintf("%d",n),S)];
   while nops(R) < n do
       S:= cat(S, seq(i,i=M+1..2*M));
       M:= 2*M;
       R:= [StringTools:-SearchAll(sprintf("%d",n),S)];
   od;
   R[n]
end proc:
map(f, [$1..100]); # Robert Israel, Jul 31 2025

Python

def a(n):
    # a(n) is the starting position of the n-th occurrence of n in
    # the string 123456789101112131415161718192021    .
    full='~'+''.join(map(str,range(1,10000)))
    def place(n,str_n,offset):
        p=full[offset:].find(str_n)+offset
        return p if n==1 else place(n-1,str_n,p+1)
    return place(n,str(n),0)
# prints the first fifty terms
print(', '.join(str(a(i)) for i in range(1,51)))