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.
a(34) = 34 + 3 + 4 = 41, a(40) = 40 + 4 = 44.
a062028 n = a007953 n + n -- Reinhard Zumkeller, Oct 11 2013
with(numtheory): for n from 1 to 100 do a := convert(n,base,10): c := add(a[i],i=1..nops(a)): printf(`%d,`,n+c); od: A062028 := n -> n+add(i,i=convert(n,base,10)) # M. F. Hasler, Nov 08 2018
Table[n + Total[IntegerDigits[n]], {n, 0, 100}]
A062028(n)=n+sumdigits(n) \\ M. F. Hasler, Jul 19 2015
def a(n): return n + sum(map(int, str(n))) print([a(n) for n in range(71)]) # Michael S. Branicky, Jan 09 2023
a004207 n = a004207_list !! n a004207_list = 1 : iterate a062028 1 -- Reinhard Zumkeller, Oct 14 2013, Sep 12 2011
read("transforms") :
A004207 := proc(n)
option remember;
if n = 0 then
1;
else
add( digsum(procname(i)),i=0..n-1) ;
end if;
end proc: # R. J. Mathar, Apr 02 2014
# second Maple program:
a:= proc(n) option remember; `if`(n<2, 1, (t->
t+add(i, i=convert(t, base, 10)))(a(n-1)))
end:
seq(a(n), n=0..60); # Alois P. Heinz, Jul 31 2022
f[s_] := Append[s, Plus @@ Flatten[IntegerDigits /@ s]]; Nest[f, {1}, 55] (* Robert G. Wilson v, May 26 2006 *)
f[n_] := n + Plus @@ IntegerDigits@n; Join[{1}, NestList[f, 1, 80]] (* Alonso del Arte, May 27 2006 *)
a(n) = { my(f(d, i) = d+vecsum(digits(d)), S=vector(n)); S[1]=1; for(k=1, n-1, S[k+1] = fold(f, S[1..k])); S } \\ Satish Bysany, Mar 03 2017
a = 1; print1(a, ", "); for(i = 1, 50, print1(a, ", "); a = a + sumdigits(a)); \\ Nile Nepenthe Wynar, Feb 10 2018
from itertools import islice
def agen():
yield 1; an = 1
while True: yield an; an += sum(map(int, str(an)))
print(list(islice(agen(), 54))) # Michael S. Branicky, Jul 31 2022
a016052 n = a016052_list !! (n-1) a016052_list = iterate a062028 3 -- Reinhard Zumkeller, Oct 14 2013
NestList[# + Total[IntegerDigits[#]] &, 3, 51] (* Jayanta Basu, Aug 11 2013 *) a[1] = 3; a[n_] := a[n] = a[n - 1] + Total@ IntegerDigits@ a[n - 1]; Array[a, 80] (* Robert G. Wilson v, Jun 27 2014 *)
a_list(nn) = { my(f(n, i) = n + vecsum(digits(n)), S=vector(nn+1)); S[1]=3; for(k=2, #S, S[k] = fold(f, S[1..k-1])); S[2..#S] } \\ Satish Bysany, Mar 04 2017
from itertools import islice def A016052_gen(): # generator of terms yield (a:=3) while True: yield (a:=a+sum(map(int,str(a)))) A016052_list = list(islice(A016052_gen(),20)) # Chai Wah Wu, Jun 16 2024
a007618 n = a007618_list !! (n-1) a007618_list = iterate a062028 5 -- Reinhard Zumkeller, Oct 14 2013
from itertools import accumulate def f(an, _): return an + sum(int(d) for d in str(an)) print(list(accumulate([5]*55, f))) # Michael S. Branicky, May 10 2021
a016096 n = a016096_list !! (n-1) a016096_list = iterate a062028 9 -- Reinhard Zumkeller, Oct 14 2013
from itertools import islice def A016096_gen(): # generator of terms a = 9 while True: yield a a += sum(int(d) for d in str(a)) A016096_list = list(islice(A016096_gen(),20)) # Chai Wah Wu, Mar 29 2022
For n=3, A016052 never meets A004207, so a(3) = -1. For n=5, A007618 meets A004207 at the 53rd term, 620, so a(5) = 53.
import Data.Maybe (fromMaybe)
a230107 = fromMaybe (-1) . f (10^5) 1 1 1 where
f k i u j v | k <= 0 = Nothing
| u < v = f (k - 1) (i + 1) (a062028 u) j v
| u > v = f (k - 1) i u (j + 1) (a062028 v)
| otherwise = Just j
read transforms; # to get digsum M:=2000; # f(s) returns the sequence k->k+digsum(k) starting at s f:=proc(s) global M; option remember; local n,k,s1; s1:=[s]; k:=s; for n from 1 to M do k:=k+digsum(k); s1:=[op(s1),k]; od: end; # g(s) returns (x,p), where x = first number in common between # f(1) and f(s), and p is the position where it occurred. # If f(1), f(s) are disjoint for M terms, returns (-1,-1) S1:=convert(f(1),set): g:=proc(s) global f,S1; local t1,p,S2,S3; S2:=convert(f(s),set); S3:= S1 intersect S2; t1:=min(S3); if (t1 = infinity) then RETURN(-1,-1); else member(t1,f(s),'p'); RETURN(t1,p-1); fi; end; [seq(g(n)[2],n=1..20)];
NestList[#+Total[IntegerDigits[#]]&,31,60] (* Harvey P. Dale, Jan 30 2020 *)
read transforms; # to get digsum M:=2000; # f(s) returns the sequence k->k+digsum(k) starting at s f:=proc(s) global M; option remember; local n,k,s1; s1:=[s]; k:=s; for n from 1 to M do k:=k+digsum(k); s1:=[op(s1),k]; od: end; # g(s) returns (x,p), where x = first number in common between # f(s) and one of f(1), f(3), f(9) and p is the position where it occurred. # If f(s) and all of f(1), f(3), f(9) are disjoint for M terms, returns (-1,-1) S1:=convert(f(1),set): S3:=convert(f(3),set): S9:=convert(f(9),set): g:=proc(s) global f,S1,S3,S9; local t1,p,T0,T1,T2; T0:=f(s): T1:=convert(T0,set); if ((s mod 9) = 3) or ((s mod 9) = 6) then T2:= T1 intersect S3; t1:=min(T2); if (t1 = infinity) then RETURN(-1,-1); else member(t1,T0,'p'); RETURN(t1,p-1); fi; elif ((s mod 9) = 0) then T2:= T1 intersect S9; t1:=min(T2); if (t1 = infinity) then RETURN(-1,-1); else member(t1,T0,'p'); RETURN(t1,p-1); fi; else T2:= T1 intersect S1; t1:=min(T2); if (t1 = infinity) then RETURN(-1,-1); else member(t1,T0,'p'); RETURN(t1,p-1); fi; fi; end; [seq(g(n)[2],n=1..45)];
a249043 n = a249043_list !! (n-1) a249043_list = iterate a062028 42 -- Reinhard Zumkeller, Oct 31 2014
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