A165449 Write the prime numbers in a string: 2357111317192329... (cf. A033308). The sequence gives the first position in the string for natural numbers.

5, 1, 2, 21, 3, 31, 4, 41, 12, 47, 5, 62, 7, 22, 77, 32, 9, 95, 11, 589, 110, 113, 1, 128, 131, 137, 63, 149, 15, 158, 8, 14, 123, 24, 2, 188, 19, 42, 72, 206, 21, 215, 23, 227, 233, 236, 25, 248, 75, 257, 78, 263, 27, 269, 275, 278, 3, 290, 29, 299, 31, 829

Offset

1,1

Comments

Same as A229190 but omitting the a(0) term.

Defined for all a by the normality of the Copeland-Erdős constant. - Aaron Weiner, Sep 19 2013

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Example

The first occurrence of "111" in the string is 5, so a(111)=5.

Maple

with(StringTools): s:="": for n from 1 to 300 do s:=cat(s, convert(ithprime(n), string)): od: seq(Search(convert(n, string), s), n=1..62); # Nathaniel Johnston, May 26 2011

Mathematica

With[{prd=Flatten[IntegerDigits/@Prime[Range[1000]]], nn=10}, Flatten[ Table[ SequencePosition[ prd, IntegerDigits[ n], 1], {n, 70}], 1]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 12 2019 *)

Prog

(Python)
from sympy import primerange
from itertools import count, takewhile
def afind(plimit):
  s = "".join(str(p) for p in primerange(1, plimit+1))
  return [1+s.find(str(n)) for n in takewhile(lambda i: str(i) in s, count(1))]
print(afind(10**4)) # Michael S. Branicky, May 01 2021

Crossrefs

Cf. A229190 (same sequence but including the a(0) term).

Cf. A031297.

Sequence in context: A318430 A318098 A318068 * A019114 A201526 A091384

Adjacent sequences: A165446 A165447 A165448 * A165450 A165451 A165452

Keyword

easy,base,nonn

Author

Rémy Sigrist, Sep 20 2009

Status

approved