A361831 a(n) is the first member of A106843 with sum of digits n.

2, 3, 13, 5, 6, 7, 17, 9, 19, 29, 39, 67, 59, 69, 79, 89, 99, 199, 389, 489, 499, 599, 699, 997, 1889, 999, 1999, 2999, 4989, 4999, 6899, 6999, 17989, 8999, 18999, 29989, 39989, 48999, 49999, 59999, 69999, 79999, 98999, 198999, 199999, 389999, 589989, 598999, 599999, 798999, 799999, 989999

Offset

2,1

Comments

If n is not divisible by 3, a(n) is the least prime with sum of digits n.

If n > 3 is divisible by 3 but not by 9, a(n) = 3*p where p is prime.

If n is divisible by 9, a(n) is divisible by 9.

Conjecture: a(n) == 9 (mod 10) for all n > 25.

Conjecture: all terms are zeroless. - Chai Wah Wu, Mar 30 2023

Links

Chai Wah Wu, Table of n, a(n) for n = 2..304

Example

a(4) = 13 because 13 is the first prime whose sum of digits is 4.
a(6) = 6 because 6 = 3*2 where 2 is prime and 6 has sum of digits 6.

Maple

f106843:= proc(t) local w; w:= padic:-ordp(t, 3); isprime(t/3^w) or t/3^w = 1 end proc;
V:= Array(2..60):  count:= 0:
for x from 2 while count < 59 do
  if f106843(x) then
    s:= convert(convert(x, base, 10), `+`);
    if s <= 60 and V[s] = 0 then V[s]:= x; count:= count+1; fi
  fi
od:
convert(V, list);

Prog

(Python)
from itertools import count
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations, partitions
from gmpy2 import digits
def A361831(n):
    for m in count((n+8)//9):
        c = (t:=10**m)
        for a, b in partitions(n, m=m, k=9, size=True):
            b[0] = (m-a)
            for s in multiset_permutations(b):
                if (lambda n:isprime(n) or n==1)(int('0'+digits(k:=int('0'+''.join(str(d) for d in s)), 3).rstrip('0'), 3)):
                    c = min(c, k)
        if c < t:
            return c # Chai Wah Wu, Mar 30-31 2023

Crossrefs

Cf. A007953, A106843.

Sequence in context: A067182 A342667 A191000 * A085402 A085400 A067523

Adjacent sequences: A361828 A361829 A361830 * A361832 A361833 A361834

Keyword

nonn,base

Author

Robert Israel, Mar 26 2023

Status

approved