A030108 -id:A030108 - cp's OEIS frontend

A030106 Base 7 reversal of n (written in base 10).

0, 1, 2, 3, 4, 5, 6, 1, 8, 15, 22, 29, 36, 43, 2, 9, 16, 23, 30, 37, 44, 3, 10, 17, 24, 31, 38, 45, 4, 11, 18, 25, 32, 39, 46, 5, 12, 19, 26, 33, 40, 47, 6, 13, 20, 27, 34, 41, 48, 1, 50, 99, 148, 197, 246, 295, 8, 57, 106, 155, 204, 253, 302, 15, 64, 113, 162, 211, 260, 309, 22, 71

Offset: 0

David W. Wilson

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A030101 - A030108, A004086.

f:= proc(n) local L,k;
  L:= convert(n,base,7);
  add(L[-i]*7^(i-1),i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, May 19 2020

Table[FromDigits[Reverse[IntegerDigits[n,7]],7],{n,0,80}] (* Harvey P. Dale, Sep 17 2013 *)

a(n,b=7)=subst(Polrev(base(n,b)),x,b) /* where */
base(n,b)={my(a=[n%b]);while(0M. F. Hasler, Nov 04 2011

A056961 Base 12 reversal of n (written in base 10).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 133, 2, 14, 26, 38, 50, 62, 74, 86, 98, 110, 122, 134, 3, 15, 27, 39, 51, 63, 75, 87, 99, 111, 123, 135, 4, 16, 28, 40, 52, 64, 76, 88, 100, 112, 124, 136, 5, 17, 29, 41, 53, 65, 77, 89, 101

Offset: 0

Henry Bottomley, Jul 18 2000

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A004086, A030101-A030108, A056960-A056963.

IntegerReverse[Range[0, 100], 12] (* Paolo Xausa, Aug 08 2024 *)

A056962 Base 16 reversal of n (written in base 10).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 17, 33, 49, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 2, 18, 34, 50, 66, 82, 98, 114, 130, 146, 162, 178, 194, 210, 226, 242, 3, 19, 35, 51, 67, 83, 99, 115, 131, 147, 163, 179, 195, 211, 227, 243, 4

Offset: 0

Henry Bottomley, Jul 18 2000

			a(17) = 17 because 17 in hexadecimal is 11, the same as its reverse.
a(18) = 33 because 18 in hexadecimal is 12, and hexadecimal 21 is 2 * 16 + 1 = 33.
a(19) = 49 because 19 in hexadecimal is 13, and hexadecimal 31 is 3 * 16 + 1 = 49.

Cf. A004086, A030101-A030108, A056960-A056963, A029730.

Table[FromDigits[Reverse[IntegerDigits[n, 16]], 16], {n, 0, 127}] (* Alonso del Arte, Sep 30 2018 *)

a(n) = fromdigits(Vecrev(digits(n, 16)), 16); \\ Michel Marcus, Sep 30 2018

A091974 Let R_{k}(n) = the digit reversal of n in base k (R_{k}(n) is written in base 10). a(n) is the number of distinct values of R_{k}(n) arising if k=2,..,n+1.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 5, 5, 5, 6, 7, 9, 9, 11, 11, 12, 11, 14, 13, 16, 16, 17, 19, 21, 19, 22, 22, 21, 23, 24, 27, 27, 27, 29, 29, 32, 29, 35, 33, 36, 32, 38, 37, 41, 39, 41, 40, 42, 41, 45, 43, 45, 46, 48, 47, 49, 50, 52, 52, 55, 53, 57, 58, 56, 57, 59, 60, 61

Offset: 0

Naohiro Nomoto, Mar 14 2004

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, Density plot of (n, R_k(n)) for n = 0..1000 and k >= 2

Cf. A004086, A030101-A030108, A056960-A056963, A181385.

rev[x_, b_]:=FromDigits[Reverse[IntegerDigits[x, b]], b]
Length /@ Union /@ Table[Table[rev[x, b], {b, 2, x + 1}], {x, 1, 200}] (* Dylan Hamilton, Oct 16 2010 *)

a(n) = #Set(apply(b -> fromdigits(Vecrev(digits(n,b)),b), [2..max(2,n+1)])) \\ Rémy Sigrist, Jan 29 2020

A055958 a(n) = n + reversal of base 9 digits of n (written in base 10).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 10, 20, 30, 40, 50, 60, 70, 80, 90, 20, 30, 40, 50, 60, 70, 80, 90, 100, 30, 40, 50, 60, 70, 80, 90, 100, 110, 40, 50, 60, 70, 80, 90, 100, 110, 120, 50, 60, 70, 80, 90, 100, 110, 120, 130, 60, 70, 80, 90, 100, 110, 120, 130, 140, 70, 80, 90

Offset: 0

Henry Bottomley, Jul 18 2000

If n has an even number of digits in base 9 then a(n) is a multiple of 10.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A030108, A056964.

Table[n+FromDigits[Reverse[IntegerDigits[n,9]],9],{n,0,70}] (* Harvey P. Dale, Sep 03 2013 *)

a(n) = n + fromdigits(Vecrev(digits(n, 9)), 9); \\ Michel Marcus, Sep 27 2018

a(n) = n + A030108(n).

A083678 Numbers m = d_1 d_2 ... d_k (in base 10) with properties that k is even and d_i + d_{k+1-i} = 10 for all i.

Original entry on oeis.org

19, 28, 37, 46, 55, 64, 73, 82, 91, 1199, 1289, 1379, 1469, 1559, 1649, 1739, 1829, 1919, 2198, 2288, 2378, 2468, 2558, 2648, 2738, 2828, 2918, 3197, 3287, 3377, 3467, 3557, 3647, 3737, 3827, 3917, 4196, 4286, 4376, 4466, 4556, 4646, 4736, 4826, 4916

Offset: 1

Zak Seidov Jun 15 2003

The two-digit terms here occur in many sequences, e.g., A066686, A081926, A017173, A030108, A043457, A052224, A061388, A084364.

			1469 and 6284 are members because 1+9=4+6=10 and 6+4=2+8=10.

Harvey P. Dale, Table of n, a(n) for n = 1..819 (All terms through 999999.)

Cf. A066686, A081926, A017173, A030108, A043457, A052224, A061388, A084364.

ok10Q[n_]:=Module[{idn=IntegerDigits[n]},idn[[1]]+idn[[4]]==idn[[2]]+idn[[3]]==10]; Join[ Select[ Range[10,99],Total[IntegerDigits[#]]==10&],Select[Range[1000,9999],ok10Q]] (* Harvey P. Dale, Oct 14 2023 *)

isok(n) = {digs = digits(n); if (#digs % 2 == 0, for (i = 1, #digs/2, if ((digs[i] + digs[#digs+1-i]) ! = 10, return (0));); return (1);); return (0);} \\ Michel Marcus, Oct 05 2013

A346113 Base-10 numbers k whose number of divisors equals the number of divisors in R(k), where k is written in all bases from base-2 to base-10 and R(k), the digit reversal of k, is read as a number in the same base.

Original entry on oeis.org

1, 9077, 10523, 10838, 30182, 58529, 73273, 77879, 83893, 244022, 303253, 303449, 304853, 329893, 332249, 334001, 334417, 335939, 336083, 346741, 374617, 391187, 504199, 512695, 516982, 595274, 680354, 687142, 758077, 780391, 792214, 854669, 946217, 948539, 995761, 1008487, 1377067, 1389341

Offset: 1

Scott R. Shannon, Jul 05 2021

There are 633 terms below 50 million and 1253 terms below 100 million. All of those have tau(k), the number of divisors of k, equal to 1, 2, 4, 8 or 16. The first term where tau(k) = 2 is n = 93836531, a prime, which is also the first term of A136634. All terms in A136634 will appear in this sequence, as will all terms in A228768(n) for n>=10. The first term with tau(k) = 4 is 9077, the first with tau(k) = 8 is 595274, and the first with tau(k) = 16 is 5170182. It is possible tau(k) must equal 2^i, with i>=0, although this is unknown.

All known terms are squarefree. - Michel Marcus, Jul 07 2021

			9077 is a term as the number of divisors of 9077 = tau(9077) = 4, and this equals the number of divisors of R(9077) when written and then read as a base-j number, with 2 <= j <= 10. See the table below for k = 9077.
.
  base | k_base         | R(k_base)      | R(k_base)_10  | tau(R(k_base)_10)
----------------------------------------------------------------------------------
   2   | 10001101110101 | 10101110110001 | 11185         | 4
   3   | 110110012      | 210011011      | 15421         | 4
   4   | 2031311        | 1131302        | 6002          | 4
   5   | 242302         | 203242         | 6697          | 4
   6   | 110005         | 500011         | 38887         | 4
   7   | 35315          | 51353          | 12533         | 4
   8   | 21565          | 56512          | 23882         | 4
   9   | 13405          | 50431          | 33157         | 4
  10   | 9077           | 7709           | 7709          | 4

Scott R. Shannon, Table of n, a(n) for n = 1..1253

Cf. A000005, A004086.
Cf. A030102, A030103, A030104, A030105, A030106, A030107, A030108.
Cf. A136634 (prime terms), A228768.
Subsequence of A062895.

Select[Range@100000,Length@Union@DivisorSigma[0,Join[{s=#},FromDigits[Reverse@IntegerDigits[s,#],#]&/@Range[2,10]]]==1&] (* Giorgos Kalogeropoulos, Jul 06 2021 *)

isok(k) = {my(t= numdiv(k)); for (b=2, 10, my(d=digits(k, b)); if (numdiv(fromdigits(Vecrev(d), b)) != t, return (0));); return(1);} \\ Michel Marcus, Jul 06 2021

A055959 n - reversal of base 9 digits of n (written in base 10).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -8, -16, -24, -32, -40, -48, -56, 16, 8, 0, -8, -16, -24, -32, -40, -48, 24, 16, 8, 0, -8, -16, -24, -32, -40, 32, 24, 16, 8, 0, -8, -16, -24, -32, 40, 32, 24, 16, 8, 0, -8, -16, -24, 48, 40, 32, 24, 16, 8, 0, -8, -16, 56, 48, 40, 32, 24, 16, 8, 0, -8, 64, 56, 48, 40, 32, 24, 16, 8, 0, 80, 0, -80, -160

Offset: 0

Henry Bottomley, Jul 18 2000

a(n) is a multiple of 8.

Cf. A030108, A056965.

Table[n-FromDigits[Reverse[IntegerDigits[n,9]],9],{n,0,120}] (* Harvey P. Dale, Dec 17 2022 *)

a(n) = n - A030108(n).

A091951 Let R_{k}(m) = the digit reversal of m in base k (R_{k}(m) is written in base 10). a(n) is the smallest m such that R_{k}(m) = n, where k >= 2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 5, 8, 6, 10, 7, 12, 7, 11, 9, 8, 10, 18, 9, 15, 9, 10, 13, 24, 10, 16, 15, 12, 11, 18, 11, 17, 12, 14, 19, 12, 13, 22, 21, 16, 13, 21, 13, 20, 15, 14, 23, 32, 14, 22, 15, 20, 17, 30, 15, 16, 15, 22, 31, 39, 16, 26, 33, 16, 20, 18, 17, 28, 21, 26, 17, 27, 17, 26

Offset: 0

Naohiro Nomoto, Mar 17 2004

Cf. A004086, A030101-A030108, A056960-A056963.

A092122 Let R_{k}(m) = the digit reversal of m in base k (R_{k}(m) is written in base 10). Sequence gives numbers m such that m = Sum_{d|m, d>1} R_{d}(m).

Original entry on oeis.org

6, 154, 310, 370, 2829, 3526, 15320, 20462, 1164789, 4336106, 5782196, 145582972

Offset: 1

Naohiro Nomoto, Mar 30 2004

			m = 154 is a term: Sum_{d|154, d>1} R_{d}(154) = 89 + 10 + 34 + 11 + 7 + 2 + 1 = 154.

Cf. A004086, A030101-A030108, A056960-A056963.

from sympy import divisors
from sympy.ntheory import digits
def fd(d, b): return sum(di*b**i for i, di in enumerate(d[::-1]))
def R(k, n): return fd(digits(n, k)[1:][::-1], k)
def ok(n):
    s = 0
    for d in divisors(n, generator=True):
        if d == 1: continue
        s += R(d, n)
        if s > n: return False
    return n == s
print([k for k in range(1, 21000) if ok(k)]) # Michael S. Branicky, Nov 14 2022

a(9)-a(12) from Michael S. Branicky, Nov 14 2022

cp's OEIS Frontend

A030106 Base 7 reversal of n (written in base 10).

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A056961 Base 12 reversal of n (written in base 10).

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A056962 Base 16 reversal of n (written in base 10).

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A091974 Let R_{k}(n) = the digit reversal of n in base k (R_{k}(n) is written in base 10). a(n) is the number of distinct values of R_{k}(n) arising if k=2,..,n+1.

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A055958 a(n) = n + reversal of base 9 digits of n (written in base 10).

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A083678 Numbers m = d_1 d_2 ... d_k (in base 10) with properties that k is even and d_i + d_{k+1-i} = 10 for all i.

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A346113 Base-10 numbers k whose number of divisors equals the number of divisors in R(k), where k is written in all bases from base-2 to base-10 and R(k), the digit reversal of k, is read as a number in the same base.

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A055959 n - reversal of base 9 digits of n (written in base 10).

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A091951 Let R_{k}(m) = the digit reversal of m in base k (R_{k}(m) is written in base 10). a(n) is the smallest m such that R_{k}(m) = n, where k >= 2.