A138792 -id:A138792 - cp's OEIS frontend

A136251 a(n) = n-th prime reduced modulo the sum of its digits.

0, 0, 0, 0, 1, 1, 1, 9, 3, 7, 3, 7, 1, 1, 3, 5, 3, 5, 2, 7, 3, 15, 6, 4, 1, 1, 3, 3, 9, 3, 7, 1, 5, 9, 9, 4, 1, 3, 13, 8, 9, 1, 4, 11, 10, 9, 3, 6, 7, 8, 1, 1, 3, 3, 5, 10, 14, 1, 5, 6, 10, 13, 7, 1, 5, 9, 2, 12, 11, 13, 1, 2, 15, 9, 18, 5, 9, 17, 1, 6, 13, 1, 7, 3, 7, 3, 7, 9, 10, 8, 8, 19, 12, 1, 15, 7, 5

Offset: 1

Odimar Fabeny, Mar 17 2008

First occurrence of k: A138792. - Robert G. Wilson v, Mar 27 2008

			2 = 2*1 + 0
3 = 3*1 + 0
5 = 5*1 + 0
7 = 7*1 + 0
11 = 2*5 + 1 (the sum of the digits of 11 is equal to 2)
13 = 4*3 + 1
17 = 8*2 + 1
19 = 10*1 + 9

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000040, A070635, A138791, A138792, A347702.

P := select(isprime, [2,seq(i,i=3..10^3,2)]):
map(p -> p mod convert(convert(p,base,10),`+`), P); # Robert Israel, Mar 05 2024

f[n_] := Block[{p = Prime@n}, Mod[p, Plus @@ IntegerDigits@p]]; Array[f, 97] (* Robert G. Wilson v, Mar 27 2008 *)

a(n) = my(p=prime(n)); p % sumdigits(p); \\ Michel Marcus, Mar 07 2023

a(n) = A070635(A000040(n)). - Michel Marcus, Mar 07 2023

More terms from Robert G. Wilson v, Mar 27 2008

A138791 Least number k such that A070635(k) = n.

Original entry on oeis.org

1, 11, 16, 15, 14, 38, 34, 29, 28, 19, 49, 76, 68, 98, 269, 79, 458, 397, 379, 299, 779, 769, 689, 898, 799, 3889, 4898, 5599, 6698, 7996, 8798, 9599, 19888, 16999, 18899, 67979, 58898, 39899, 59998, 49999, 89789, 189989, 89998, 98999, 489898, 298999

Offset: 0

Robert G. Wilson v, Mar 29 2008

A070635(a(n)) = n and A070635(m) <> n for m < a(n).

Least k such that k mod A007953(k) = n. - Robert Israel, Dec 29 2015

			a(2) = 16: 1+6 = 7 and 16 mod 7 = 2. - _Robert Israel_, Dec 30 2015

Robert G. Wilson v and Robert Israel, Table of n, a(n) for n = 0..514(n = 0..79 from Robert G. Wilson v)

Cf. A007953,A070635, A138792.

Cf. A199262.

a199263 n = (fromJust $ elemIndex n a070635_list) + 1
-- Reinhard Zumkeller, Nov 07 2011

extend:= proc(d, x, sx)
global A, nmin;
local y, n, tmax;
if d = 0 then
    n:= x mod sx;
    if not assigned(A[n]) then
       A[n]:= x;
       if n = nmin then
         for nmin from n while assigned(A[nmin]) do od:
       fi;
    fi
else
  tmax:= 9*d + sx;
  if nmin >= tmax then return fi;
  for y from max(0, nmin + 10 - tmax) to 9 do
    procname(d-1,10*x+y,sx+y)
  od:
fi
end proc:
A[0]:= 1:
nmin:= 1:
for d from 2 while nmin < 101 do
   extend(d,0,0)
od:
seq(A[i],i=0..nmin-1); # Robert Israel, Dec 29 2015

t = Table[0, {100}]; Do[ a = Mod[n, Plus @@ IntegerDigits@n]; If[a < 100 && t[[a + 1]] == 0, t[[a + 1]] = n; Print[{a, n}]], {n, 2^31}]
lnk[n_]:=Module[{k=1},While[Mod[k,Total[IntegerDigits[k]]]!=n,k++];k]; Array[lnk, 50, 0] (* Harvey P. Dale, Oct 11 2014 *)

Definition corrected by Robert Israel, Dec 29 2015

cp's OEIS Frontend

A136251 a(n) = n-th prime reduced modulo the sum of its digits.

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