A359248 a(n) is the first number that is the start of a string of exactly n consecutive numbers in A358350.

3, 11, 42, 32, 20, 154, 130, 1240, 515, 1033, 610, 3101, 103, 4010, 56379, 31809, 35212, 23103, 7413, 12101, 1011, 204, 10391, 92109, 25013, 812819, 75099, 8493016, 437016, 775009, 287017, 8029, 457014, 10503, 26148108, 10997, 27445016, 286092, 231135007, 480014

Offset: 1

Author

Robert Israel, Dec 22 2022

Keywords

• nonn
• base

Comments

a(n) is the least k such that k, k+1, ..., k+n-1 are in A358350 but k-1 and k+n are not.

Examples

			a(3) = 42 because the three consecutive numbers 42, 43 and 44 are in A358350 but 41 and 45 are not, and this is the first string of exactly three consecutive numbers in A358350.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..71
• Michael S. Branicky, All terms below 3.4*10^10

Crossrefs

Cf. A358350.

Programs

Maple

f:= proc(n) local L; L:= convert(n,base,10); n + convert(L,`+`)+convert(L,`*`) end proc:
S:= select(`<=`,map(f,{$1..10^6}),10^6):
S:= sort(convert(S,list)):
V:= Vector(27):
a:= 1:
for x from 2 to nops(S) do
  if S[x] - S[x-1] > 1 then
    v:= x-a;
    if v <= 27 and V[v] = 0 then V[v]:= S[a]; count:= count+1; fi;
    a:= x;
  fi
od:
convert(V,list);

Python

from math import prod
from itertools import islice
def sp(n): d = list(map(int, str(n))); return sum(d) + prod(d)
def agen(increment=10**6):
    S, L, U, adict, rl, n = set(), 1, increment, dict(), 0, 1
    while True:
        S |= set(i + sp(i) for i in range(L, U))
        for i in range(L, U):
            if i in S: rl += 1
            else:
                if rl not in adict:
                    adict[rl] = i - rl
                    while n in adict: yield adict[n]; n += 1
                rl = 0
        S -= set(range(L, U))
        L, U = U, U + increment
print(list(islice(agen(), 34))) # Michael S. Branicky, Dec 23 2022

Extensions

a(28)-a(40) from Michael S. Branicky, Dec 22 2022