A055018 Numbers k such that k and k+1 are modest (cf. A054986).

411, 811, 1421, 2036, 2044, 2054, 3054, 4036, 4044, 4054, 8036, 12036, 16036, 20036, 24036, 28036, 32036, 40011, 40044, 50054, 50074, 80011, 88296, 100110, 100270, 100369, 120296, 120404, 140021, 144242, 176296, 200044, 200270, 200369

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..2000 (terms 1..250 from Reinhard Zumkeller)

Example

2036 is modest because Mod[2036, 36] = 20. 2037 is modest because Mod[2037, 037] = 2. Hence 2036 is this pair's modest twin representative.

Mathematica

mdstQ[n_, d_]:=Module[{c}, c=(FromDigits/@TakeDrop[IntegerDigits[n], d]); Mod[n, c[[2]]/.(0->1)]==c[[1]]]; SequencePosition[Table[ If[ Total[ Boole[ Table[ mdstQ[n, d], {d, IntegerLength[n]-1}]]]>0, 1, 0], {n, 201000}], {1, 1}][[;; , 1]] (* Harvey P. Dale, Nov 22 2025 *)

Prog

(Haskell)
import Data.List (elemIndices)
a055018 n = a055018_list !! (n-1)
a055018_list = map (a054986 . (+ 1)) $ elemIndices 1 $
               zipWith (-) (tail a054986_list) a054986_list
-- Reinhard Zumkeller, Mar 26 2012
(Python)
from itertools import count, islice
def modest(n):
    pow10 = 1
    while (t:= divmod(n, pow10))[0]:
        if t[1] and n%t[1] == t[0]: return True
        pow10 *= 10
    return False
def agen(start=1): # generator of terms >= start
    modestk = modest(start-1)
    for k in count(start):
        modestk1, modestk = modestk, modest(k)
        if modestk and modestk1: yield k-1
print(list(islice(agen(), 38))) # Michael S. Branicky, Dec 08 2025

Crossrefs

Cf. A054986.

Sequence in context: A212710 A187991 A090123 * A201844 A105211 A081378

Adjacent sequences: A055015 A055016 A055017 * A055019 A055020 A055021

Keyword

base,nonn

Author

Hans Havermann, May 31 2000

Status

approved