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

1,1

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.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..71

Michael S. Branicky, All terms below 3.4*10^10

Example

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.

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);

Prog

(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

Crossrefs

Cf. A358350.

Sequence in context: A358426 A096147 A225431 * A099489 A077830 A106460

Adjacent sequences: A359245 A359246 A359247 * A359249 A359250 A359251

Keyword

nonn,base

Author

Robert Israel, Dec 22 2022

Extensions

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

Status

approved