A138792 - OEIS

%I #26 Mar 07 2023 15:37:46

%S 2,11,67,23,89,53,83,29,173,19,197,193,337,167,269,79,757,397,379,479,

%T 3677,769,997,6967,1699,3889,9857,7867,6959,9949,16987,9887,49697,

%U 47599,18899,67979,73999,56999,197699,49999,159899,189989,98899,98999,988877

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

%C First occurrence of n in A136251.

%H David A. Corneth, <a href="/A138792/b138792.txt">Table of n, a(n) for n = 0..181</a> (first 74 terms from Robert G. Wilson v)

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

%p V:= Array(0..50): count:= 0: p:= 1:

%p while count < 51 do

%p   p:= nextprime(p);

%p   s:= convert(convert(p,base,10),`+`);

%p   v:= p mod s;

%p   if v <= 50 and V[v] = 0 then V[v]:= p; count:= count+1;  fi

%p od:

%p convert(V,list); # _Robert Israel_, Mar 07 2023

%t 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}]

%t 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 *)

%o (PARI) a(n) = my(p=2); while ((p % sumdigits(p)) != n, p=nextprime(p+1)); p; \\ _Michel Marcus_, Mar 07 2023

%o (Python)

%o from sympy import nextprime

%o from itertools import islice

%o def agen(): # generator of terms

%o     adict, n, p = dict(), 0, 2

%o     while True:

%o         v = p%sum(map(int, str(p)))

%o         if v not in adict: adict[v] = p

%o         while n in adict: yield adict[n]; n += 1

%o         p = nextprime(p)

%o print(list(islice(agen(), 45))) # _Michael S. Branicky_, Mar 07 2023

%Y Cf. A136251, A138791.

%K base,nonn

%O 0,1

%A _Robert G. Wilson v_, Mar 28 2008

%E Name corrected by _Robert Israel_, Mar 07 2023