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

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

Author

Robert G. Wilson v, Mar 28 2008

Keywords

• base
• nonn

Comments

First occurrence of n in A136251.

Examples

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

Links

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

Crossrefs

Cf. A136251, A138791.

Programs

Maple

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

Mathematica

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 *)

PARI

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

Python

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

Extensions

Name corrected by Robert Israel, Mar 07 2023