A138791 -id:A138791 - cp's OEIS frontend

A070635 a(n) = n mod (sum of digits of n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 4, 3, 2, 1, 0, 9, 0, 0, 2, 3, 0, 4, 2, 0, 8, 7, 0, 3, 2, 3, 6, 3, 0, 7, 5, 3, 0, 1, 0, 1, 4, 0, 6, 3, 0, 10, 0, 3, 3, 5, 0, 5, 1, 9, 6, 3, 0, 5, 6, 0, 4, 10, 6, 2, 12, 9, 0, 7, 0, 3, 8, 3, 11, 7, 3, 15, 0, 0, 2, 6, 0, 7, 2, 12, 8

Offset: 1

Reinhard Zumkeller, May 13 2002

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007953.

Cf. A199238.

a070635 n = n `mod` (a007953 n)
-- Reinhard Zumkeller, Apr 07 2011

[n mod (&+Intseq(n)): n in [1..100]]; // Vincenzo Librandi, Dec 30 2015

Table[Mod[n,Total[IntegerDigits[n]]],{n,100}] (* Harvey P. Dale, Mar 11 2013 *)

a(n) = n % sumdigits(n); \\ Michel Marcus, Dec 30 2015

a(A005349(n)) = 0. - Reinhard Zumkeller, Mar 10 2008
A188641(n) = A000007(a(n)); a(A065877(n)) > 0. - Reinhard Zumkeller, Apr 07 2011
a(A138791(n)) = n and a(m) <> n for m < A138791(n). - Reinhard Zumkeller, Nov 07 2011

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

Original entry on oeis.org

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

A138792 Least prime, p, such that p mod (sum of the digits of p) = n.

Original entry on oeis.org

2, 11, 67, 23, 89, 53, 83, 29, 173, 19, 197, 193, 337, 167, 269, 79, 757, 397, 379, 479, 3677, 769, 997, 6967, 1699, 3889, 9857, 7867, 6959, 9949, 16987, 9887, 49697, 47599, 18899, 67979, 73999, 56999, 197699, 49999, 159899, 189989, 98899, 98999, 988877

Offset: 0

Robert G. Wilson v, Mar 28 2008

First occurrence of n in A136251.

			a(2) = 67 = 13*5+2 <--> 67 (mod 13) = 2.

David A. Corneth, Table of n, a(n) for n = 0..181 (first 74 terms from Robert G. Wilson v)

Cf. A136251, A138791.

V:= Array(0..50): count:= 0: p:= 1:
while count < 51 do
  p:= nextprime(p);
  s:= convert(convert(p,base,10),`+`);
  v:= p mod s;
  if v <= 50 and V[v] = 0 then V[v]:= p; count:= count+1;  fi
od:
convert(V,list); # Robert Israel, Mar 07 2023

f[n_] := Block[{p = Prime@ n}, Mod[p, Plus @@ IntegerDigits@ p]]; t = Table[0, {1000}]; Do[ a = f@n; If[a < 1000 && t[[a + 1]] == 0, t[[a + 1]] = Prime@ n; Print[{a, Prime@n}]], {n, 503200000}]
lp[n_]:=Module[{p=2},While[Mod[p,Total[IntegerDigits[p]]]!=n,p= NextPrime[ p]];p]; Array[lp,50,0] (* Harvey P. Dale, Jan 15 2019 *)

a(n) = my(p=2); while ((p % sumdigits(p)) != n, p=nextprime(p+1)); p; \\ Michel Marcus, Mar 07 2023

from sympy import nextprime
from itertools import islice
def agen(): # generator of terms
    adict, n, p = dict(), 0, 2
    while True:
        v = p%sum(map(int, str(p)))
        if v not in adict: adict[v] = p
        while n in adict: yield adict[n]; n += 1
        p = nextprime(p)
print(list(islice(agen(), 45))) # Michael S. Branicky, Mar 07 2023

Name corrected by Robert Israel, Mar 07 2023

A199262 Smallest m such that A199238(m) = n.

Original entry on oeis.org

1, 3, 11, 15, 59, 95, 223, 255, 1007, 1919, 4091, 6143, 16379, 28671, 61439, 65535, 261119, 516095, 1048571, 1966079, 4128767, 8380415, 16769023, 25165823, 67108799, 134184959, 268434431, 469762047, 1073741819, 2013265919, 4160749567, 4294967295, 17163091967

Offset: 0

Reinhard Zumkeller, Nov 04 2011

nonn

A199238(a(n)) = n and A199238(m) <> n for m < a(n).

Cf. A138791.

a199262 n = (fromJust $ elemIndex n a199238_list) + 1

a(24)-a(32) from Donovan Johnson, Nov 05 2011

cp's OEIS Frontend

A070635 a(n) = n mod (sum of digits of n).

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

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A138792 Least prime, p, such that p mod (sum of the digits of p) = n.

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A199262 Smallest m such that A199238(m) = n.

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