This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
The third Champernowne prime A176942(3) = 123456789101112131415161 is obtained by concatenating the digits of the numbers 1,2,3,4,...,17, and then dropping the final digit; thus a(3) = 17.
a007908 = read . concatMap show . enumFromTo 1 :: Integer -> Integer -- Reinhard Zumkeller, Dec 13 2012
[Seqint(Reverse(&cat[Reverse(Intseq(k)): k in [1..n]])): n in [1..17]]; // Bruno Berselli, May 27 2011
A055642 := proc(n) max(1, ilog10(n)+1) ; end: A007908 := proc(n) if n = 1 then 1; else A007908(n-1)*10^A055642(n)+n ; fi ; end: seq(A007908(n),n=1..12) ; # R. J. Mathar, May 31 2008 # second Maple program: a:= proc(n) a(n):= `if`(n=0, 0, parse(cat(a(n-1), n))) end: seq(a(n), n=1..22); # Alois P. Heinz, Jan 12 2021
Table[FromDigits[Flatten[IntegerDigits[Range[n]]]], {n, 20}] (* Alonso del Arte, Sep 19 2012 *)
FoldList[#2 + #1 10^IntegerLength[#2] &, Range[20]] (* Eric W. Weisstein, Nov 06 2015 *)
FromDigits /@ Flatten /@ IntegerDigits /@ Flatten /@ Rest[FoldList[List, {}, Range[20]]] (* Eric W. Weisstein, Nov 04 2015 *)
FromDigits /@ Flatten /@ IntegerDigits /@ Rest[FoldList[Append, {}, Range[20]]] (* Eric W. Weisstein, Nov 04 2015 *)
a[1]:1$ a[n]:=a[n-1]*10^floor(log(10*n)/log(10))+n$ makelist(a[n],n,1,17); /* Bruno Berselli, May 27 2011 */
a(n)=my(s="");for(k=1,n,s=Str(s,k));eval(s) \\ Charles R Greathouse IV, Sep 19 2012
A007908(n,a=0)={for(d=1,#Str(n),my(t=10^d);for(k=t\10,min(t-1,n),a=a*t+k));a} \\ M. F. Hasler, Sep 30 2015
def a(n): return int("".join(map(str, range(1, n+1))))
print([a(n) for n in range(1, 18)]) # Michael S. Branicky, Jan 12 2021
from functools import reduce def A007908(n): return reduce(lambda i,j:i*10**len(str(j))+j,range(1,n+1)) # Chai Wah Wu, Feb 27 2023
f[0] = 0; f[n_Integer] := 10^(Floor[Log[10, n]] + 1)*f[n - 1] + n; Do[If[PrimeQ[FromDigits[Take[IntegerDigits[f[n]], n]]], Print[n]], {n, 1, 3000}]
Cases[FromDigits /@ Rest[FoldList[Append, {}, RealDigits[N[ChampernowneNumber[], 1000]][[1]]]], p_?PrimeQ :> IntegerLength[p]] (* Eric W. Weisstein, Nov 04 2015 *)
from itertools import count, islice from sympy import isprime def A071620_gen(): # generator of terms c, l = 0, 0 for n in count(1): for d in str(n): c = 10*c+int(d) l += 1 if isprime(c): yield l A071620_list = list(islice(A071620_gen(),5)) # Chai Wah Wu, Feb 27 2023
a(1) is 82 since the 155-digit number 828180...54321 is prime. a(2) is 37765 since the 177719-digit number 377653776437763...54321 is (a probable) prime.
# uses A001292gen() and imports from A001292 from sympy import isprime def agen(): yield from filter(isprime, A001292gen()) print(list(islice(agen(), 10))) # Michael S. Branicky, Jul 01 2022
a(2) = 3 as 11_2 is prime. a(3) = 5 as 12_3 is prime. a(4) = 109 as 1231_4 is prime. a(5) = 7 as 12_5 is prime. a(6) = 18796638871 as 12345101112131_6 is prime. a(7) = 131870666077 as 12345610111213_7 is prime. a(8) = 83 as 123_8 is prime. a(9) = 11 as 12_9 is prime. a(10) = 1234567891 as 1234567891_10 is prime. See A176942. a(11) = 13 as 12_11 is prime. a(12) = 24677 as 12345_12 is prime.
a(6) = 8 as A252043(6) = 123456 = 2^6 * 3 * 643, which has 8 prime divisors.
Lim=65;ch=RealDigits[ChampernowneNumber[], 10, Lim][[1]];Table[PrimeOmega[FromDigits[Take[ch,n]]],{n,Lim}] (* James C. McMahon, Sep 19 2024 *)
Concatenation 123 has primes 23 and 3 ending at the 3, and 23 is in the sequence first since its substring starts first.
import sympy
def concat_up_to_k(k):
return ''.join(str(i) for i in range(1, k + 1))
def primes_in_substrings(s):
A383790 = []
prime_set = set()
for i in range(1, len(s) + 1):
for j in range(i):
substring = s[j:i]
if substring[0] != '0':
num = int(substring)
if sympy.isprime(num) and num not in prime_set:
A383790.append(num)
prime_set.add(num)
return A383790
k = 17
number_string = concat_up_to_k(k)
A383790 = primes_in_substrings(number_string)
print(A383790)
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