cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-26 of 26 results.

A347689 A347688(n)/9.

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, 11, 11, 21, 31, 41, 51, 61, 71, 81, 91, 11, 0, 11, 22, 33, 44, 55, 66, 77, 88
Offset: 0

Views

Author

N. J. A. Sloane, Sep 23 2021

Keywords

Crossrefs

Cf. A347688.

Programs

Formula

a(n) = A297330(n) for n<=99. - R. J. Mathar, Sep 27 2021
a(n) = A037904(n) for n<=99. - R. J. Mathar, Sep 27 2021

Extensions

More than the usual number of terms are shown in order to distinguish this from similar sequences.

A383305 a(n) is number of n-digit nonnegative integers whose difference between the largest and smallest digits is equal to the arithmetic mean of its digits.

Original entry on oeis.org

1, 6, 39, 266, 1730, 11361, 74809, 494194, 3273132, 21730506, 144588345, 964050593, 6440655572, 43111601819, 289112380019, 1942335481170, 13072051432742, 88125501965430, 595077180675348, 4024698113281006, 27261843502415806, 184931926767687963, 1256249015578188517, 8545135121520262849, 58198759816476208605
Offset: 1

Views

Author

Stefano Spezia, Apr 22 2025

Keywords

Crossrefs

Cf. A037904, A054054, A054055, A371383, A371384, A383304.

Programs

  • Mathematica
    a[n_]:=Module[{c=KroneckerDelta[n,1]}, For[k=10^(n-1), k<=10^n, k++, If[Max[d=IntegerDigits[k]]-Min[d]==Mean[d], c++]]; c]; Array[a,7]
  • Python
    def A383305(n):
    if n<=1: return n
    s={(k,k,k):1 for k in range(1,10)}
    for i in range(n-1):
        snew={}
        for (h,l,t),v in s.items():
            for d in range(10):
                p=(max(h,d),min(l,d),t+d)
                if p in snew:
                    snew[p]+=v
                else:
                    snew[p]=v
        s=snew
    return sum( v for (h,l,t),v in s.items() if n*(h-l)==t) # Bert Dobbelaere, Apr 25 2025

Extensions

More terms from Bert Dobbelaere, Apr 25 2025

A234512 Numbers n = d(0)d(1)d(2)...d(r) such that d(i) is the number of differences |d(i)-d(i-1)| equal to i in n, i = 1,2,...,r.

Original entry on oeis.org

110, 311000, 2301000, 3003000, 3120000, 42100000, 410300000, 430100000
Offset: 1

Views

Author

Michel Lagneau, Dec 27 2013

Keywords

Comments

In the decimal system a differential autobiographical number is a natural number such that d(0) is the number of differences |d(i)-d(i-1)| = 0, d(1) is the number of differences |d(i)-d(i-1)| = 1, and so on.
Property of this sequence: the sum of the decimal digits of a(n) equals length(a(n))-1.
It is possible to extend this problem by counting the differences |d(i)-d(i-1)| with the additional difference |d(r)-d(1)|. So we find a new sequence b(n) = 22100, 311100, 3022000, 20402000, 31310000, 40004000, 422010000, 430110000 with the property that the sum of the decimal digits of b(n) equals length(b(n)).

Examples

			311000 is in the sequence because the differential digits are:
|1-3| = 2;
|1-1| = 0;
|0-1| = 1;
|0-0| = 0;
|0-0| = 0, and
0 appears three times => 3;
1 appears one time => 1;
2 appears one time  => 1;
3 appears zero time => 0;
4 appears zero time => 0;
5 appears zero time => 0, hence a(2) = 311000.

Links

Crossrefs

Cf. A037904, A046043, A108551, A138480.

Programs

  • Maple
    with(numtheory):for n from 10 to 10^10 do:T:=array(0..9):for k from 0 to 9 do:T[k]:=0:od:x:=convert(n,base,10):n1:=nops(x):for i from 1 to n1-1 do:a:=abs(x[i]-x[i+1]):T[a]:=T[a]+1:od:s:=sum('T[i]*10^(10-i-1)','i'=0..9): for u from 9 by -1 to 1 do:if T[0]<>0 and irem(s,10^u)=0 and s/10^u = n then print(n):else fi:od:od:

A383304 Nonnegative integers whose difference between the largest and smallest digits is equal to the arithmetic mean of its digits.

Original entry on oeis.org

0, 13, 26, 31, 39, 62, 93, 123, 132, 144, 213, 225, 231, 246, 252, 264, 267, 276, 288, 312, 321, 348, 369, 384, 396, 414, 426, 438, 441, 462, 483, 522, 624, 627, 639, 642, 672, 693, 726, 762, 828, 834, 843, 882, 936, 963, 1133, 1223, 1232, 1313, 1322, 1331, 1344, 1434, 1443
Offset: 1

Views

Author

Stefano Spezia, Apr 22 2025

Keywords

Examples

			144 is a term since 4 - 1 = 3 = (1 + 4 + 4)/3.

Crossrefs

Cf. A037904, A054054, A054055, A179239, A371383, A371384, A383305.
Subsequence of A061383.

Programs

  • Mathematica
    Select[Range[0,1500], Max[d=IntegerDigits[#]]-Min[d]==Mean[d] &]
  • Python
    def ok(n): return sum(d:=list(map(int, str(n)))) == (max(d) - min(d))*len(d)
print([k for k in range(1500) if ok(k)]) # Michael S. Branicky, Apr 23 2025

A383306 Nonnegative integers whose difference between the largest and smallest digits is equal to the mode of its digits.

Original entry on oeis.org

0, 101, 110, 112, 121, 202, 211, 220, 224, 242, 303, 330, 336, 363, 404, 422, 440, 448, 484, 505, 550, 606, 633, 660, 707, 770, 808, 844, 880, 909, 990, 1011, 1022, 1033, 1044, 1055, 1066, 1077, 1088, 1099, 1101, 1110, 1112, 1121, 1202, 1211, 1220, 1223, 1232
Offset: 1

Views

Author

Stefano Spezia, Apr 22 2025

Keywords

Comments

It includes only terms with unimodal digits.

Examples

			363 is a term since 6 - 3 = 3 is equal to the mode of {3, 3, 6}.

Crossrefs

Cf. A037904, A054054, A054055, A115353, A383307.

Programs

  • Mathematica
    Select[Range[0,1400], {Max[d=IntegerDigits[#]]-Min[d]}==Commonest[d] &]

A383307 a(n) is number of n-digit nonnegative integers whose difference between the largest and smallest digits is equal to the mode of its digits.

Original entry on oeis.org

1, 0, 30, 631, 8318, 84939, 762621, 6836799, 66714966, 698183347, 7345264685, 74862560359, 738289921745, 7152117119827, 69258386123495, 678852874461343, 6757612542040310, 67956663939884115, 684414144298352061, 6858156111567293583, 68247431544857431593, 675967074881581484903
Offset: 1

Views

Author

Stefano Spezia, Apr 22 2025

Keywords

Links

Crossrefs

Cf. A037904, A054054, A054055, A115353, A383306.

Programs

  • Mathematica
    a[n_]:=Module[{c=KroneckerDelta[n,1]}, For[k=10^(n-1), k<=10^n, k++, If[{Max[d=IntegerDigits[k]]-Min[d]}==Commonest[d], c++]]; c]; Array[a,6]

Formula

Conjecture: lim_{n->oo} a(n+1)/a(n) = 10. - Stefano Spezia, Apr 26 2025

Extensions

More terms from Bert Dobbelaere, Apr 25 2025
Previous Showing 21-26 of 26 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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