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A138792
Least prime, p, such that p mod (sum of the digits of p) = n.
3
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
0,1
COMMENTS
First occurrence of n in A136251.
LINKS
David A. Corneth, Table of n, a(n) for n = 0..181 (first 74 terms from Robert G. Wilson v)
EXAMPLE
a(2) = 67 = 13*5+2 <--> 67 (mod 13) = 2.
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 *)
PROG
(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
CROSSREFS
Sequence in context: A185627 A216585 A245277 * A058056 A266579 A063768
KEYWORD
base,nonn
AUTHOR
Robert G. Wilson v, Mar 28 2008
EXTENSIONS
Name corrected by Robert Israel, Mar 07 2023
STATUS
approved