A037904 -id:A037904 - cp's OEIS frontend

A366962 Numbers whose difference between the largest and smallest digits is equal to 5.

16, 27, 38, 49, 50, 61, 72, 83, 94, 105, 116, 126, 136, 146, 150, 156, 161, 162, 163, 164, 165, 166, 205, 216, 227, 237, 247, 250, 257, 261, 267, 272, 273, 274, 275, 276, 277, 305, 316, 327, 338, 348, 350, 358, 361, 368, 372, 378, 383, 384, 385, 386, 387, 388

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms of this sequence is 29*6^(n-1) - 49*5^(n-1) + 5*4^n.

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).

Select[Range[400],Max[d=IntegerDigits[#]]-Min[d]==5 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 5; \\ Michel Marcus, Nov 05 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 5
print([k for k in range(400) if ok(k)]) # Michael S. Branicky, Oct 30 2023

A366963 Numbers whose difference between the largest and smallest digits is equal to 6.

Original entry on oeis.org

17, 28, 39, 60, 71, 82, 93, 106, 117, 127, 137, 147, 157, 160, 167, 171, 172, 173, 174, 175, 176, 177, 206, 217, 228, 238, 248, 258, 260, 268, 271, 278, 282, 283, 284, 285, 286, 287, 288, 306, 317, 328, 339, 349, 359, 360, 369, 371, 379, 382, 389, 393, 394, 395, 396, 397, 398, 399

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms of this sequence is 27*7^(n-1) - 47*6^(n-1) + 4*5^n.

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).

Select[Range[400],Max[d=IntegerDigits[#]]-Min[d]==6 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 6; \\ Michel Marcus, Nov 05 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 6
print([k for k in range(400) if ok(k)]) # Michael S. Branicky, Oct 30 2023

A366964 Numbers whose difference between the largest and smallest digits is equal to 7.

Original entry on oeis.org

18, 29, 70, 81, 92, 107, 118, 128, 138, 148, 158, 168, 170, 178, 181, 182, 183, 184, 185, 186, 187, 188, 207, 218, 229, 239, 249, 259, 269, 270, 279, 281, 289, 292, 293, 294, 295, 296, 297, 298, 299, 307, 318, 329, 370, 381, 392, 407, 418, 429, 470, 481, 492

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms is 23*8^(n-1) - 41*7^(n-1) + 2^n*3^(n+1).

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366965 (difference = 8), A366966 (difference = 9).

Select[Range[500],Max[d=IntegerDigits[#]]-Min[d]==7 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 7; \\ Michel Marcus, Nov 05 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 7
print([k for k in range(500) if ok(k)]) # Michael S. Branicky, Oct 30 2023

A366965 Numbers whose difference between the largest and smallest digits is equal to 8.

Original entry on oeis.org

19, 80, 91, 108, 119, 129, 139, 149, 159, 169, 179, 180, 189, 191, 192, 193, 194, 195, 196, 197, 198, 199, 208, 219, 280, 291, 308, 319, 380, 391, 408, 419, 480, 491, 508, 519, 580, 591, 608, 619, 680, 691, 708, 719, 780, 791, 800, 801, 802, 803, 804, 805, 806, 807, 808, 810

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms of this sequence is 17*9^(n-1) - 31*8^(n-1) + 2*7^n.

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366966 (difference = 9).

Select[Range[810],Max[d=IntegerDigits[#]]-Min[d]==8 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 8; \\ Michel Marcus, Nov 05 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 8
print([k for k in range(900) if ok(k)]) # Michael S. Branicky, Oct 30 2023

A366966 Numbers whose difference between the largest and smallest digits is equal to 9.

Original entry on oeis.org

90, 109, 190, 209, 290, 309, 390, 409, 490, 509, 590, 609, 690, 709, 790, 809, 890, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 920, 930, 940, 950, 960, 970, 980, 990, 1009, 1019, 1029, 1039, 1049, 1059, 1069, 1079, 1089, 1090, 1091, 1092, 1093, 1094, 1095

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms of this sequence is 9*10^(n-1) - 17*9^(n-1) + 8^n.

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8).

Select[Range[1095],Max[d=IntegerDigits[#]]-Min[d]==9 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 9; \\ Michel Marcus, Nov 05 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 9
print([k for k in range(1100) 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 A366966_gen(): # generator of terms
    return chain.from_iterable(sorted(int(''.join(str(d) for d in t)) for c in combinations_with_replacement(range(10),l) for t in multiset_permutations((0,9)+c) if t[0]) for l in count(0))
A366966_list = list(islice(A366966_gen(),30)) # Chai Wah Wu, Nov 10 2023

A040163 a(n) is the absolute value of (the first digit of n minus the last digit of n).

Original entry on oeis.org

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, 1, 0, 1, 2, 3, 4, 5

Offset: 1

Felice Russo

			a(371) = abs(3 - 1) = 2.
a(567) = abs(5 - 7) = 2.

David F. Marrs, Table of n, a(n) for n = 1..10000

Cf. A000030 (first digit of n), A010879 (last digit of n).

Cf. A037904, A040114, A040115, A040997.

Array[Abs[First@ # - Last@ #] &@ IntegerDigits@ # &, 106] (* Michael De Vlieger, Oct 15 2018 *)

a(n) = my(digs = digits(n)); abs(digs[1] - digs[#digs]); \\ Michel Marcus, Sep 27 2013

apply( {A040163(n)=abs(n\10^logint(n+!n,10)-n%10)}, [0..111]) \\ M. F. Hasler, Apr 22 2024

for n in range(1,51): print(abs(int(str(n)[0])-int(str(n)[-1]))) # David F. Marrs, Oct 14 2018

a(n) = abs(floor(n / 10 ^ floor(log_10(n))) - (n - floor(n / 10) * 10)) - David F. Marrs, Oct 14 2018

A366958 Numbers whose difference between the largest and smallest digits is equal to 1.

Original entry on oeis.org

10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 100, 101, 110, 112, 121, 122, 211, 212, 221, 223, 232, 233, 322, 323, 332, 334, 343, 344, 433, 434, 443, 445, 454, 455, 544, 545, 554, 556, 565, 566, 655, 656, 665, 667, 676, 677, 766, 767, 776, 778, 787, 788

Offset: 1

Stefano Spezia, Oct 30 2023

The number of n-digit terms of this sequence is 17*A000225(n-1).

Cf. A000225, A037904.

Cf. A010785 (difference = 0), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).

Select[Range[800],Max[d=IntegerDigits[#]]-Min[d]==1 &]

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 1; \\ Michel Marcus, Oct 30 2023

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 1
print([k for k in range(800) if ok(k)]) # Michael S. Branicky, Oct 30 2023

# faster version for large terms
from itertools import count, islice, product
def agen(diff=1): # generator of terms; change diff for A366960-A366966
    for digits in count(2):
        s = set()
        for lo in range(10-diff):
            hi = lo + diff
            allowed = list(range(lo, hi+1))
            for p in product(allowed, repeat=digits):
                if p[0]==0 or lo not in p or hi not in p: continue
                s.add(int("".join(map(str, p))))
        yield from sorted(s)
print(list(islice(agen(), 60))) # Michael S. Branicky, Oct 30 2023

A040114 List of absolute values of differences between digits of 10, 11, 12, ..., listed digit by digit.

Original entry on oeis.org

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, 1, 1, 2, 1, 3, 1, 4, 1, 5

Offset: 10

Felice Russo

Start with the empty sequence. For n = 10, 11, 12, ... do the following. Let the decimal expansion of n be abcd...efg, say. Append the numbers |a-b|, |b-c|, |c-d|, ... |e-f|, |f-g| to the sequence.

The offset is slightly misleading since for n > 99 the index n is in no direct relation with the number whose digits are used to produce a(n), in contrast to A040115 where all digit-differences of n are concatenated, and leading zeros don't appear. For example, a(100) = 1 and a(101) = 0 are the two differences between the digits of 100. Similarly, a(100 + 2k) corresponds to the difference between first and second digit of 100 + k. Therefore, a(120) = 0. - M. F. Hasler, Nov 09 2019

			From _M. F. Hasler_, Nov 09 2019: (Start)
The first term is the difference between digits of 10, which is 1.
The second term is the difference between digits of 11, which is 0.
The 100th term is the difference between the first two digits of 100, 1-0 = 1.
The 101st term is the difference between the last two digits of 100, 0-0 = 0.
The 120th term is the difference between the first two digits of 110, 1-1 = 0: Here "leading zeros" are preserved, in contrast to A040115 where all digit-wise differences of any n are concatenated to one term, and leading zeros disappear.
(End)
When we reach n = 371, for example, we append 4 and 6 to the sequence.

T. D. Noe, Table of n, a(n) for n = 10..1902

Cf. A037904, A040115, A040163, A040997.

Flatten[Table[Abs[Differences[IntegerDigits[n]]],{n,10,200}]] (* Harvey P. Dale, Jun 28 2021 *)

Definition clarified by N. J. A. Sloane, Aug 19 2008.

Name edited by M. F. Hasler, Nov 09 2019

A115300 Greatest digit of n * least digit of n.

Original entry on oeis.org

1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8

Offset: 1

Rick L. Shepherd, Jan 20 2006

a(101) = 0 and A111707(101) = 1, but all previous terms match.

a(n) = A169669(n) for n <= 100.

			a(3) = 3 * 3 = 9, a(232) = 3 * 2 = 6, a(1889009898) = 9 * 0 = 0.

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

Cf. A037904 (greatest-least), A115299 (greatest+least), A111707.

Cf. A054054, A054055, A169669.

a115300 n = a054054 n * a054055 n  -- Reinhard Zumkeller, Apr 29 2015

Array[Max[#] * Min[#] &@ IntegerDigits[#] &, 81] (* James C. McMahon, Aug 18 2024 *)

a(n) = my(d=digits(n)); vecmin(d)*vecmax(d); \\ Michel Marcus, Aug 18 2024

def a(n): d = list(map(int, str(n))); return max(d) * min(d)
print([a(n) for n in range(1, 82)]) # Michael S. Branicky, Dec 12 2023

a(n) = A054054(n)*A054055(n). - Reinhard Zumkeller, Apr 29 2015

A115299 Greatest digit of n + least digit of n. Different from A088133.

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, Jan 20 2006

a(101) = 1 and A088133(101) = 2, but all previous terms match.

			a(1) = 1 + 1 = 2, a(232) = 3 + 2 = 5, a(1889009898) = 9 + 0 = 9.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A037904 (greatest-least), A115300 (greatest*least), A088133 (first+last).

Array[Max[#] + Min[#] &@ IntegerDigits[#] &, 120] (* Michael De Vlieger, Dec 12 2023 *)

def a(n): d = list(map(int, str(n))); return max(d) + min(d)
print([a(n) for n in range(1, 87)]) # Michael S. Branicky, Dec 12 2023

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A366962 Numbers whose difference between the largest and smallest digits is equal to 5.

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A366963 Numbers whose difference between the largest and smallest digits is equal to 6.

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A366964 Numbers whose difference between the largest and smallest digits is equal to 7.

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A366965 Numbers whose difference between the largest and smallest digits is equal to 8.

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A366966 Numbers whose difference between the largest and smallest digits is equal to 9.

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A040163 a(n) is the absolute value of (the first digit of n minus the last digit of n).

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A366958 Numbers whose difference between the largest and smallest digits is equal to 1.

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A040114 List of absolute values of differences between digits of 10, 11, 12, ..., listed digit by digit.

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