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.
David Cleaver has authored 7 sequences.
a[n_] := Prime[(n/2^IntegerExponent[n, 2] + 1)/2]; Array[a, 100] (* Amiram Eldar, Mar 21 2025 *)
a(12)=28 since 1234567891011121110987654321 has 28 digits.
a[n_]:=IntegerLength[FromDigits[Flatten[IntegerDigits/@Join[Range[n], Reverse[Range[n-1]]]]]]; Array[a,63] (* Stefano Spezia, Apr 16 2025 *)
a(n)={my(t=logint(n,10)+1); 2*n*t-2*(10^t-1)/9+t}
def a(n): return ((n*(t:=len(str(n)))-(10**t-1)//9)<<1) + t print([a(n) for n in range(1, 64)]) # Michael S. Branicky, May 02 2023
a(3) = 71 because 71 is the smallest prime factor of A098129(3) = 122333. a(7) = 1141871 because 1141871 is the smallest prime factor of A098129(7) = 1223334444555556666667777777.
from sympy import primefactors def A358275(n): return min(primefactors(int(''.join(str(j)*j for j in range(1,n+1))))) if n&1 else 2 # Chai Wah Wu, Apr 15 2023
For n = 4, a(4) = 10, because A098129(4) = 1223334444. For n = 10, a(10) = 65, because A098129(10) = 12233344445555566666677777778888888899999999910101010101010101010.
a:= proc(n) a(n):= `if`(n<1, 0, a(n-1)+n*length(n)) end: seq(a(n), n=1..100); # Alois P. Heinz, Mar 23 2023
a(n) = {my(x=logint(n,10)+1);x*n*(n+1)/2 - ((100^x-1)/99 - (10^x-1)/9)/2}
vector(100, i, a(i))
def a(n):
d = len(str(n))
m = 10**d
return d*n*(n+1)//2 - ((m-11)*m + 10)//198
print([a(n) for n in range(1, 55)]) # Michael S. Branicky, Mar 24 2023 modified Mar 29 2023
# faster for generating initial segment of sequence from itertools import count, islice def agen(s=0): yield from (s:=s+n*len(str(n)) for n in count(1)) print(list(islice(agen(), 60))) # Michael S. Branicky, Mar 24 2023
a(3) = 2 because the 3rd odd integer 5 equals 101 in binary, and removing the least significant consecutive 1's gives us 10 in binary = 2 in decimal. a(4) = 1 because the 4th odd integer 7 equals 111 in binary, and removing all except the initial 1 gives us 1 in binary = 1 in decimal. a(5) = 4 because the 5th odd integer 9 equals 1001 in binary, and removing the least significant consecutive 1's gives us 100 in binary = 4 in decimal. a(6) = 2 because the 6th odd integer 11 equals 1011 in binary, and removing the least significant consecutive 1's gives us 10 in binary = 2 in decimal.
f[n_] := n/2^IntegerExponent[n, 2]; a[n_] := Module[{f1=f[n]}, If[f1==1, 1, f1-1]]; Array[a, 60] (* Amiram Eldar, Dec 01 2018 *)
print_list(n)={my(i);for(i=1,n,print1(max(1,i>>valuation(i,2)-1),","));}
a(n)={max(1, n>>valuation(n,2)-1)} \\ Andrew Howroyd, Dec 01 2018
def print_list(n):
for i in range(1,n,2):
z=i
while z>1 and z%2 == 1:
z = (z-1)/2
print(z)
def a(n):
z = 2*n - 1
while z>1 and z%2 == 1:
z = (z-1)/2
print(z)
def A322250(n): s = bin(2*n-1)[2:].rstrip('1') return int(s,2) if s != '' else 1 # Chai Wah Wu, Jan 02 2019
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