A037904 -id:A037904 - cp's OEIS frontend

A072817 Accumulative sum of the greatest digit of n minus the least digit of n (A037904) <= 10^n.

1, 286, 4621, 56980, 640663, 6904678, 72722233, 755339992, 7774461355, 79520082490, 809705785165, 8217213032524, 83178920046367, 840306174900622, 8475694265094817, 85380606857454976, 859192675118710099, 8638686211723117474, 86794540082486097589, 871513270875022245748

Offset: 1

Benoit Cloitre and Robert G. Wilson v, Aug 09 2002

Let b(n) = sum( A037904(k),{k=1..n}), then the lim b(n)/n -> 9. Reason, as the number of digits increases, then the likelihood of the maximum digit -> 9 and the minimum digits -> 0 becomes one.

Andrew Howroyd, Table of n, a(n) for n = 1..200

Cf. A037904.

f[n_] := Block[{d = IntegerDigits[n]}, Max[d] - Min[d]]; s = 0; k = 0; Do[ While[k != 10^n, k++; s = s + f[k]]; Print[s], {n, 1, 8}]

a(n)={1 + sum(w=1, n, sum(k=1, 9, (10-k)*k*((k+1)^w - 2*k^w + (k-1)^w) - k*((k+1)^(w-1) - k^(w-1))))} \\ Andrew Howroyd, Jan 28 2020

a(n) = 1 + Sum_{w=1..n} Sum_{k=1..9} (10-k)*k*((k+1)^w - 2*k^w + (k-1)^w) - k*((k+1)^(w-1) - k^(w-1)). - Andrew Howroyd, Jan 28 2020

a(9)-a(12) from Donovan Johnson, Apr 09 2010

Terms a(13) and beyond from Andrew Howroyd, Jan 28 2020

A072830 Absolute value of 2b(n)-9n, where b(n) = accumulative sum of the greatest digit of n minus the least digit of n (A037904).

Original entry on oeis.org

9, 18, 27, 36, 45, 54, 63, 72, 81, 88, 97, 104, 109, 112, 113, 112, 109, 104, 97, 102, 109, 118, 125, 130, 133, 134, 133, 130, 125, 128, 133, 140, 149, 156, 161, 164, 165, 164, 161, 162, 165, 170, 177, 186, 193, 198, 201, 202, 201, 200, 201, 204, 209, 216

Offset: 1

Benoit Cloitre and Robert G. Wilson v, Aug 09 2002

Cf. A037904.

f[n_] := Block[{d = IntegerDigits[n]}, Max[d] - Min[d]]; b[n_] := b[n] = b[n - 1] + f[n]; b[1] = 0; a[n_] := a[n] = Abs[2b[n] - 9*n]; Table[ a[n], {n, 1, 65}]
gdmld[n_]:=Module[{idn=IntegerDigits[n]},Max[idn]-Min[idn]]; Module[ {nn=60,gd}, gd=Accumulate[gdmld/@Range[nn]];Abs[ 2*Last[#]- 9*First[ #]]&/@Thread[{Range[nn],gd}]]

Let b(n) = sum( A037904(k), {k=1..n}), a(n) = |2*b(n) - 9*n|.

Definition clarified by Harvey P. Dale, May 21 2014

A000030 Initial digit of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

N. J. A. Sloane, Simon Plouffe

When n - a(n)*10^[log_10 n] >= 10^[(log_10 n) - 1], where [] denotes floor, or when n < 100 and 10|n, n is the concatenation of a(n) and A217657(n). - Reinhard Zumkeller, Oct 10 2012, improved by M. F. Hasler, Nov 17 2018, and corrected by Glen Whitney, Jul 01 2022

Equivalent definition: The initial a(0) = 0 is followed by each digit in S = {1,...,9} once. Thereafter, repeat 10 times each digit in S. Then, repeat 100 times each digit in S, etc.

			23 begins with a 2, so a(23) = 2.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

David W. Wilson, Table of n, a(n) for n = 0..10000
A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.

Cf. A010879 (final digit of n).
Cf. A061681, A130571, A109453, A134010, A052038.
Cf. A002993, A089951, A002994, A143464, A098174, A098175, A072543, A072544, A073600, A073601, A037904. - Reinhard Zumkeller, Aug 17 2008

a000030 = until (< 10) (`div` 10) -- Reinhard Zumkeller, Feb 20 2012, Feb 11 2011

[Intseq(n)[#Intseq(n)]: n in [1..100]]; // Vincenzo Librandi, Nov 17 2018

A000030 := proc(n)
    if n = 0 then
        0;
    else
        convert(n,base,10) ;
        %[-1] ;
    end if;
end proc:
seq(A000030(n),n=0..200) ;# N. J. A. Sloane, Feb 10 2017

Join[{0},First[IntegerDigits[#]]&/@Range[90]] (* Harvey P. Dale, Mar 01 2011 *)
Table[Floor[n/10^(Floor[Log10[n]])], {n, 1, 50}] (* G. C. Greubel, May 16 2017 *)
Table[NumberDigit[n,IntegerLength[n]-1],{n,0,100}] (* Harvey P. Dale, Aug 29 2021 *)

a(n)=if(n<10,n,a(n\10)) \\ Mainly for illustration.

A000030(n)=n\10^logint(n+!n,10) \\ Twice as fast as a(n)=digits(n)[1]. Before digits() was added in PARI v.2.6.0 (2013), one could use, e.g., Vecsmall(Str(n))[1]-48. - M. F. Hasler, Nov 17 2018

def a(n): return int(str(n)[0])
print([a(n) for n in range(85)]) # Michael S. Branicky, Jul 01 2022

a(n) = [n / 10^([log_10(n)])] where [] denotes floor and log_10(n) is the logarithm is base 10. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 07 2001

a(n) = k for k*10^j <= n < (k+1)*10^j for some j. - M. F. Hasler, Mar 23 2015

A010785 Repdigit numbers, or numbers whose digits are all equal.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 333333, 444444, 555555, 666666

Offset: 0

N. J. A. Sloane

Complement of A139819. - David Wasserman, May 21 2008
Subsequence of A134336 and of A178403. - Reinhard Zumkeller, May 27 2010
Subsequence of A193460. - Reinhard Zumkeller, Jul 26 2011
Intersection of A009994 and A009996. - David F. Marrs, Sep 29 2018
Beiler (1964) called these numbers "monodigit numbers". The term "repdigit numbers" was used by Trigg (1974). - Amiram Eldar, Jan 21 2022

Albert H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, p. 83.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Eric F. Bravo, Carlos A. Gómez and Florian Luca, Product of Consecutive Tribonacci Numbers With Only One Distinct Digit, J. Int. Seq., Vol. 22 (2019), Article 19.6.3.
Eric Fernando Bravo, On concatenations of Padovan and Perrin numbers, Math. Commun. (2023) Vol 28, 105-119.
Mahadi Ddamulira, Repdigits as sums of three balancing numbers, Mathematica Slovaca, (2019), hal-02405969.
Mahadi Ddamulira, Padovan numbers that are concatenations of two distinct repdigits, arXiv:2003.10705 [math.NT], 2020.
Mahadi Ddamulira, Tribonacci numbers that are concatenations of two repdigits, hal-02547159, Mathematics [math] / Number Theory [math.NT], 2020.
Mahadi Ddamulira, Padovan numbers that are concatenations of two distinct repdigits, Mathematica Slovaca, Vol. 71, No. 2 (2021), pp. 275-284.
Bart Goddard and Jeremy Rouse, Sum of two repdigits a square, arXiv:1607.06681 [math.NT], 2016. Mentions this sequence.
Bir Kafle, Florian Luca and Alain Togbé, Triangular Repblocks, Fibonacci Quart., Vol. 56, No. 4 (2018), pp. 325-328.
Bir Kafle, Florian Luca and Alain Togbé, Pentagonal and heptagonal repdigits, Annales Mathematicae et Informaticae, Vol. 52 (2020), pp. 137-145.
Benedict Vasco Normenyo, Bir Kafle, and Alain Togbé, Repdigits as Sums of Two Fibonacci Numbers and Two Lucas Numbers, Integers, Vol. 19 (2019), Article A55.
Salah Eddine Rihane and Alain Togbé, Repdigits as products of consecutive Padovan or Perrin numbers, Arab. J. Math., Vol. 10 (2021), pp. 469-480.
Charles W. Trigg, Infinite sequences of palindromic triangular numbers, The Fibonacci Quarterly, Vol. 12, No. 2 (1974), pp. 209-212.
Eric Weisstein's World of Mathematics, Repdigit.
Wikipedia, Repdigit.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,-10).

Cf. A000005, A009994, A009996, A010879, A037904, A047842, A059995, A065444, A134336, A139819, A151949, A178401, A178403, A180410, A193459, A193460, A202022, A227362, A244112.

a010785 n = a010785_list !! n
a010785_list = 0 : r [1..9] where
   r (x:xs) = x : r (xs ++ [10*x + x `mod` 10])
-- Reinhard Zumkeller, Jul 26 2011

[(n-9*Floor((n-1)/9))*(10^Floor((n+8)/9)-1)/9: n in [0..50]]; // Vincenzo Librandi, Nov 10 2014

A010785 := proc(n)
    (n-9*floor(((n-1)/9)))*((10^(floor(((n+8)/9)))-1)/9) ;
end proc:
seq(A010785(n), n = 0 .. 100); # Robert Israel, Nov 09 2014

fQ[n_]:=Module[{id=IntegerDigits[n]}, Length[Union[id]]==1]; Select[Range[0,10000], fQ] (* Vladimir Joseph Stephan Orlovsky, Dec 29 2010 *)
Union[FromDigits/@Flatten[Table[PadRight[{},i,n],{n,0,9},{i,6}],1]] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,-10}, {0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88},40] (* Harvey P. Dale, Dec 28 2011 *)
Union@ Flatten@ Table[k (10^n - 1)/9, {k, 0, 9}, {n, 6}] (* Robert G. Wilson v, Oct 09 2014 *)
Table[(n - 9 Floor[(n-1)/9]) (10^Floor[(n+8)/9] - 1)/9, {n, 0, 50}] (* José de Jesús Camacho Medina, Nov 06 2014 *)

a(n)=10^((n+8)\9)\9*((n-1)%9+1) \\ Charles R Greathouse IV, Jun 15 2011

nxt(n,t=n%10)=if(t<9,n*(t+1),n*10+9)\t \\ Yields the term a(k+1) following a given term a(k)=n. M. F. Hasler, Jun 24 2016

is(n)={1==#Set(digits(n))}
inv(n) = 9*#Str(n) + n%10 - 9 \\ David A. Corneth, Jun 24 2016

def a(n): return 0 if n == 0 else int(str((n-1)%9+1)*((n-1)//9+1))
print([a(n) for n in range(55)]) # Michael S. Branicky, Dec 29 2021

print([0]+[int(d*r) for r in range(1, 7) for d in "123456789"]) # Michael S. Branicky, Dec 29 2021

# without string operations
def a(n): return 0 if n == 0 else (10**((n-1)//9+1)-1)//9*((n-1)%9+1)
print([a(n) for n in range(55)]) # Michael S. Branicky, Nov 03 2023

A037904(a(n)) = 0. - Reinhard Zumkeller, Dec 14 2007
A178401(a(n)) > 0. - Reinhard Zumkeller, May 27 2010
From Reinhard Zumkeller, Jul 26 2011: (Start)
For n > 0: A193459(a(n)) = A000005(a(n)).
for n > 10: a(n) mod 10 = floor(a(n)/10) mod 10.
A010879(n) = A010879(A059995(n)). (End)
A202022(a(n)) = 1. - Reinhard Zumkeller, Dec 09 2011
a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=6, a(7)=7, a(8)=8, a(9)=9, a(10)=11, a(11)=22, a(12)=33, a(13)=44, a(14)=55, a(15)=66, a(16)=77, a(17)=88, a(n) = 11*a(n-9) - 10*a(n-18). - Harvey P. Dale, Dec 28 2011
A151949(a(n)) = 0; A180410(a(n)) = A227362(a(n)). - Reinhard Zumkeller, Jul 09 2013
a(n) = (n - 9*floor((n-1)/9))*(10^floor((n+8)/9) - 1)/9. - José de Jesús Camacho Medina, Nov 06 2014
G.f.: x*(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7+9*x^8)/((1-x^9)*(1-10*x^9)). - Robert Israel, Nov 09 2014
A047842(a(n)) = A244112(a(n)). - Reinhard Zumkeller, Nov 11 2014
Sum_{n>=1} 1/a(n) = (7129/2520) * A065444 = 3.11446261209177581335... - Amiram Eldar, Jan 21 2022

Name clarified by Jon E. Schoenfield, Nov 10 2023

A040115 Concatenate absolute values of differences between adjacent digits of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1

Offset: 0

Felice Russo

Let the decimal expansion of n be abcd...efg, say. Then a(n) has decimal expansion |a-b| |b-c| |c-d| ... |e-f| |f-g|. Leading zeros in a(n) are omitted.
From M. F. Hasler, Nov 09 2019: (Start)
This sequence coincides with A080465 up to a(109) but is thereafter completely different.
Eric Angelini calls a(n) the "ghost" of the number n and considers iterations of n -> n +- a(n) depending on parity of a(n), cf. A329200 and A329201. (End)

			a(371) = 46, for example.
a(110) = 01 = 1, while A080465(110) = 10 - 1 = 9. - _M. F. Hasler_, Nov 09 2019

T. D. Noe, Table of n, a(n) for n = 0..10000
E. Angelini, The Ghost Iteration, Personal blog "Cinquante signes", Nov 2019
E. Angelini, The Ghost Iteration, Personal blog "Cinquante signes", Nov 2019 [Cached copy, pdf file, with permission]

Cf. A010785, A037904, A040114, A040163, A040997.

Cf. A329200, A329201: iterations of n +- a(n).

Table[FromDigits[Abs[Differences[IntegerDigits[n]]]],{n,110}] (* Harvey P. Dale, Dec 16 2021 *)

apply( A040115(n)=fromdigits(abs((n=digits(n+!n))[^-1]-n[^1])), [10..199]) \\ Works for all n >= 0. - M. F. Hasler, Nov 09 2019

a(n) = 0 iff n is a repdigit >= 11 (A010785). - Bernard Schott, May 09 2022

Definition clarified by N. J. A. Sloane, Aug 19 2008
Name edited by M. F. Hasler, Nov 09 2019
Terms a(0) = a(1) = ... = a(9) = 0 prepended by Max Alekseyev, Jul 26 2024

A040997 Absolute value of first digit of n minus sum of other digits of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Offset: 1

Felice Russo

This is different from |A055017(n)| = |(x1 + x3 + ...) - (x2 + x4 + ...)|, where x1,...,xk are the digits of n. - M. F. Hasler, Nov 09 2019

			a(371) = |3-7-1| = 5.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A037904, A040114, A040115, A040163, A055017.

Cf. A000030, A007953, A217657.

a040997 n = abs $ a000030 n - a007953 (a217657 n) -- Reinhard Zumkeller, Oct 10 2012

apply( A040997(n)={abs(vecsum(n=digits(n))-n[1]*2)}, [1..199]) \\ M. F. Hasler, Nov 09 2019

If decimal expansion of n is x1 x2 ... xk then a(n) = |x1-x2-x3- ... -xk|.

a(n) = abs(A000030(n) - A007953(A217657(n))). - Reinhard Zumkeller, Oct 10 2012

Name edited and incorrect formula deleted by M. F. Hasler, Nov 09 2019

A064834 If n (in base 10) is d_1 d_2 ... d_k then a(n) = Sum_{i = 1..[k/2] } |d_i - d_{k-i+1}|.

Original entry on oeis.org

Offset: 0

N. J. A. Sloane, Oct 25 2001

Might be called the Palindromic Deviation (or PD(n)) of n, since it measures how far n is from being a palindrome. - W. W. Kokko, Mar 13 2013

a(A002113(n)) = 0; a(A029742(n)) > 0; A136522(n) = A000007(a(n)). - Reinhard Zumkeller, Sep 18 2013

			a(456) = | 4 - 6 | = 2, a(4567) = | 4 - 7 | + | 5 - 6 | = 4.

N. J. A. Sloane, Table of n, a(n) for n = 0..10000
Index entries for sequences related to palindromes

Cf. A037904, A040163, A064844.

Cf. A031298, A037888.

a064834 n = sum $ take (length nds `div` 2) $
                  map abs $ zipWith (-) nds $ reverse nds
   where nds = a031298_row n
-- Reinhard Zumkeller, Sep 18 2013

f:=proc(n)
local t1,t2,i;
t1:=convert(n,base,10);
t2:=nops(t1);
add( abs(t1[i]-t1[t2+1-i]),i=1..floor(t2/2) );
end;
[seq(f(n),n=0..120)]; # N. J. A. Sloane, Mar 24 2013

f[n_] := (k = IntegerDigits[n]; l = Length[k]; Sum[ Abs[ k[[i]] - k[[l - i + 1]]], {i, 1, Floor[l/2] } ] ); Table[ f[n], {n, 0, 100} ]

from sympy import floor, ceiling
def A064834(n):
    x, y = str(n), 0
    lx2 = len(x)/2
    for a,b in zip(x[:floor(lx2)],x[:ceiling(lx2)-1:-1]):
        y += abs(int(a)-int(b))
    return y
# Chai Wah Wu, Aug 09 2014

More terms from Vladeta Jovovic, Matthew Conroy and Robert G. Wilson v, Oct 26 2001

A366959 Numbers whose difference between the largest and smallest digits is equal to 2.

Original entry on oeis.org

13, 20, 24, 31, 35, 42, 46, 53, 57, 64, 68, 75, 79, 86, 97, 102, 113, 120, 123, 131, 132, 133, 200, 201, 202, 210, 213, 220, 224, 231, 234, 242, 243, 244, 311, 312, 313, 321, 324, 331, 335, 342, 345, 353, 354, 355, 422, 423, 424, 432, 435, 442, 446, 453, 456, 464, 465, 466

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms of this sequence is (46*3^n - 93*2^n + 48)/6.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).

F:= proc(d) local L,i;
   L:= select(t -> max(t) = 2 and min(t) = 0, map(convert,[$3^d..2*3^d-1],base,3));
   L:= map(t -> add(t[-i-1]*10^(i-1),i=1..nops(t)-1),L);
   L:= map(t -> seq(t+i*(10^d-1)/9,i=0..7), L);
   op(sort(select(t -> t >= 10^(d-1), L)));
end proc:
F(2), F(3), F(4); # Robert Israel, Nov 10 2023

Select[Range[500],Max[d=IntegerDigits[#]]-Min[d]==2 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 2; \\ Michel Marcus, Nov 05 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 2
print([k for k in range(500) if ok(k)]) # Michael S. Branicky, Oct 30 2023

from itertools import chain, count, islice, combinations_with_replacement
from sympy.utilities.iterables import multiset_permutations
def A366959_gen(): # generator of terms
    return chain.from_iterable(sorted(int(''.join(str(d) for d in t)) for a in range(8) for c in combinations_with_replacement(range(a,a+3),l) for t in multiset_permutations((a,a+2)+c) if t[0]) for l in count(0))
A366959_list = list(islice(A366959_gen(),30)) # Chai Wah Wu, Nov 10 2023

A366960 Numbers whose difference between the largest and smallest digits is equal to 3.

Original entry on oeis.org

14, 25, 30, 36, 41, 47, 52, 58, 63, 69, 74, 85, 96, 103, 114, 124, 130, 134, 141, 142, 143, 144, 203, 214, 225, 230, 235, 241, 245, 252, 253, 254, 255, 300, 301, 302, 303, 310, 314, 320, 325, 330, 336, 341, 346, 352, 356, 363, 364, 365, 366, 411, 412, 413, 414

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms of this sequence is 27*4^(n-1) - 41*3^(n-1) + 7*2^n.

Stefano Spezia, Table of n, a(n) for n = 1..10000

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).

Select[Range[415],Max[d=IntegerDigits[#]]-Min[d]==3 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 3; \\ Michel Marcus, Nov 05 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 3
print([k for k in range(420) if ok(k)]) # Michael S. Branicky, Oct 30 2023

from itertools import chain, count, islice, combinations_with_replacement
from sympy.utilities.iterables import multiset_permutations
def A366960_gen(): # generator of terms
    return chain.from_iterable(sorted(int(''.join(str(d) for d in t)) for a in range(7) for c in combinations_with_replacement(range(a,a+4),l) for t in multiset_permutations((a,a+3)+c) if t[0]) for l in count(0))
A366960_list = list(islice(A366960_gen(),30)) # Chai Wah Wu, Nov 10 2023

A366961 Numbers whose difference between the largest and smallest digits is equal to 4.

Original entry on oeis.org

15, 26, 37, 40, 48, 51, 59, 62, 73, 84, 95, 104, 115, 125, 135, 140, 145, 151, 152, 153, 154, 155, 204, 215, 226, 236, 240, 246, 251, 256, 262, 263, 264, 265, 266, 304, 315, 326, 337, 340, 347, 351, 357, 362, 367, 373, 374, 375, 376, 377, 400, 401, 402, 403, 404, 410

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms is 29*5^(n-1) - 47*4^(n-1) + 2*3^(n+1).

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366960 (difference = 3), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).

Select[Range[410],Max[d=IntegerDigits[#]]-Min[d]==4 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 4; \\ Michel Marcus, Nov 05 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 4
print([k for k in range(411) if ok(k)]) # Michael S. Branicky, Oct 30 2023

cp's OEIS Frontend

A072817 Accumulative sum of the greatest digit of n minus the least digit of n (A037904) <= 10^n.

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A072830 Absolute value of 2*b(n)-9*n, where b(n) = accumulative sum of the greatest digit of n minus the least digit of n (A037904).

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A000030 Initial digit of n.

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A010785 Repdigit numbers, or numbers whose digits are all equal.

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A040115 Concatenate absolute values of differences between adjacent digits of n.

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A040997 Absolute value of first digit of n minus sum of other digits of n.

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A072830 Absolute value of 2b(n)-9n, where b(n) = accumulative sum of the greatest digit of n minus the least digit of n (A037904).