A061909 -id:A061909 - cp's OEIS frontend

A129967 a(n) = A061909(n)^2.

0, 1, 4, 9, 100, 121, 144, 169, 400, 441, 484, 900, 961, 10000, 10201, 10404, 10609, 12100, 12321, 12544, 12769, 14400, 14641, 14884, 16900, 40000, 40401, 40804, 44100, 44521, 44944, 48400, 48841, 90000, 90601, 96100, 96721, 1000000, 1002001, 1004004, 1006009

Offset: 1

N. J. A. Sloane, Jun 13 2007

nonn

A129968 a(n) = sum of digits of A061909(n).

Original entry on oeis.org

1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 4, 2, 3, 4, 3, 4, 5, 4, 5, 3, 4, 4, 5, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 4, 5, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 5, 3, 4, 5, 4, 5, 6, 5, 4, 5, 2, 3, 4, 3, 4, 5, 4, 5, 6, 3, 4, 5, 4, 5, 5, 6, 4, 5, 6, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 3, 4, 2, 3

Offset: 1

N. J. A. Sloane, Jun 13 2007

T. D. Noe, Table of n, a(n) for n=1..5000

A129969 a(n) = A061909(n) with digits reversed.

Original entry on oeis.org

1, 2, 3, 1, 11, 21, 31, 2, 12, 22, 3, 13, 1, 101, 201, 301, 11, 111, 211, 311, 21, 121, 221, 31, 2, 102, 202, 12, 112, 212, 22, 122, 3, 103, 13, 113, 1, 1001, 2001, 3001, 101, 1101, 2101, 3101, 201, 1201, 2201, 301, 1301, 11, 1011, 2011

Offset: 1

N. J. A. Sloane, Jun 13 2007

T. D. Noe, Table of n, a(n) for n=1..5000

Rest[IntegerReverse/@Select[Range[0,1200],IntegerReverse[#^2]==IntegerReverse[#]^2&]] (* Harvey P. Dale, Dec 01 2024 *)

A123977 Complement of A061909 (skinny numbers).

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86

Offset: 1

N. J. A. Sloane, Jul 29 2010

Index entries for sequences related to carryless arithmetic

A130596 Partial sums of skinny numbers (A061909).

Original entry on oeis.org

1, 3, 6, 16, 27, 39, 52, 72, 93, 115, 145, 176, 276, 377, 479, 582, 692, 803, 915, 1028, 1148, 1269, 1391, 1521, 1721, 1922, 2124, 2334, 2545, 2757, 2977, 3198, 3498, 3799, 4109, 4420, 5420, 6421, 7423, 8426, 9436, 10447, 11459, 12472, 13492, 14513, 15535

Offset: 1

Jonathan Vos Post, Jun 17 2007

The skinny partial sums of skinny numbers begin: a(1) = 1, a(2) = 3. The primes in the sequence begin: a(2) = 3, a(15) = 479, a(15) = 1721, a(38) = 6421, a(52) = 20899. The perfect powers in the sequence begin a(4) = 16 = 2^4, a(5) = 27 = 3^3, a(24) = 1521 = 39^2.

			a(36) = 4420 = 1+2+3+10+11+12+13+20+21+22+30+31+100+101+102+103+110+111+112+113+120+121+122+130+200+201+202+210+211+212+220+221+300+301+310+311

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Accumulate[Select[Range[0,1200],IntegerReverse[#^2]==IntegerReverse[#]^2&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 02 2017 *)

A159952 Skinny numbers (A061909) containing no 3's.

Original entry on oeis.org

0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1200, 1201, 1202, 1210, 1211, 1212

Offset: 1

N. J. A. Sloane, Jul 29 2010

a(n) first differs from A007089(n-1) at a(27) = 1000, which does not equal 222 = A007089(26). - Jason Kimberley, Dec 13 2012

Index entries for sequences related to carryless arithmetic

A169939 Skinny numbers (A061909) containing no 2's.

Original entry on oeis.org

0, 1, 3, 10, 11, 13, 30, 31, 100, 101, 103, 110, 111, 113, 130, 300, 301, 310, 311, 1000, 1001, 1003, 1010, 1011, 1013, 1030, 1031, 1100, 1101, 1103, 1110, 1111, 1113, 1130, 1300, 1301, 3000, 3001, 3010, 3011, 3100, 3101, 3110, 3111, 10000, 10001, 10003, 10010

Offset: 1

N. J. A. Sloane, Jul 29 2010

Index entries for sequences related to carryless arithmetic

A224792 Smallest skinny number (A061909) with digit sum n.

Original entry on oeis.org

0, 1, 2, 3, 13, 113, 1113, 11113, 1011113, 101011113, 1101111211, 110101111211, 100110101111211, 10101010101101122, 1011111111100000013, 1010111111111000000022, 111000010111000111111111, 1010110111101110100000011111, 1111111110010101100001100000102

Offset: 0

Reiner Moewald, Apr 18 2013

The smallest m >= 0 with sum of digits of (m) = n and sum of digits of (m^2) = (sum of digits of (m))^2.

There are infinitely many natural numbers m >= 0 with sum of digits of (m) = n and sum of digits of (m^2) = (sum of digits of (m))^2.

Hiroaki Yamanouchi, Table of n, a(n) for n = 0..19

Cf. A061909.

DS[n_] := Total[IntegerDigits[n]]; nn = 10; t = Table[0, {nn}]; n = 0; found = 0; While[n++; r = FromDigits[IntegerDigits[n, 4]]; found < nn, If[DS[r]^2 == DS[r^2] && DS[r] <= nn && t[[DS[r]]] == 0, t[[DS[r]]] = r;  found++; Print[r]]]; Join[{0}, t] (* T. D. Noe, Apr 18 2013 *)

a(n) > 2/9 * 10^(n/2) for n > 4. - Charles R Greathouse IV, Apr 18 2013

a(10) corrected and a(11) added by T. D. Noe, Apr 18 2013
a(12)-a(13) from Donovan Johnson, Apr 19 2013
a(14) from Donovan Johnson, Apr 24 2013
a(15)-a(18) from Hiroaki Yamanouchi, Aug 28 2014

A069967 Duplicate of A061909.

Original entry on oeis.org

1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 30, 31, 100, 101, 102, 103, 110, 111, 112, 113

Offset: 0

dead

A169942 Number of Golomb rulers of length n.

Original entry on oeis.org

1, 1, 3, 3, 5, 7, 13, 15, 27, 25, 45, 59, 89, 103, 163, 187, 281, 313, 469, 533, 835, 873, 1319, 1551, 2093, 2347, 3477, 3881, 5363, 5871, 8267, 9443, 12887, 14069, 19229, 22113, 29359, 32229, 44127, 48659, 64789, 71167, 94625, 105699, 139119, 151145, 199657

Offset: 1

N. J. A. Sloane, Aug 01 2010

nonn

Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?
Leading entry in row n of triangle in A169940. Also the number of Sidon sets A with min(A) = 0 and max(A) = n. Odd for all n since {0,n} is the only symmetric Golomb ruler, and reversal preserves the Golomb property. Bounded from above by A032020 since the ruler {0 < r_1 < ... < r_t < n} gives rise to a composition of n: (r_1 - 0, r_2 - r_1, ... , n - r_t) with distinct parts. - Tomas Boothby, May 15 2012
Also the number of compositions of n such that every restriction to a subinterval has a different sum. This is a stronger condition than all distinct consecutive subsequences having a different sum (cf. A325676). - Gus Wiseman, May 16 2019

			For n=2, there is one Golomb Ruler: {0,2}.  For n=3, there are three: {0,3}, {0,1,3}, {0,2,3}. - _Tomas Boothby_, May 15 2012
From _Gus Wiseman_, May 16 2019: (Start)
The a(1) = 1 through a(8) = 15 compositions such that every restriction to a subinterval has a different sum:
  (1)  (2)  (3)   (4)   (5)   (6)    (7)    (8)
            (12)  (13)  (14)  (15)   (16)   (17)
            (21)  (31)  (23)  (24)   (25)   (26)
                        (32)  (42)   (34)   (35)
                        (41)  (51)   (43)   (53)
                              (132)  (52)   (62)
                              (231)  (61)   (71)
                                     (124)  (125)
                                     (142)  (143)
                                     (214)  (152)
                                     (241)  (215)
                                     (412)  (251)
                                     (421)  (341)
                                            (512)
                                            (521)
(End)

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..99
T. Pham, Enumeration of Golomb Rulers (Master's thesis), San Francisco State U., 2011.
Eric Weisstein's World of Mathematics, Golomb Ruler.
Index entries for sequences related to carryless arithmetic
Index entries for sequences related to Golomb rulers

Related to thickness: A169940-A169954, A061909.
Related to Golomb rulers: A036501, A054578, A143823.
Row sums of A325677.
Cf. A000079, A103295, A103300, A108917, A143824, A325466, A325545, A325676, A325678, A325679, A325683, A325686.

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@ReplaceList[#,{_,s__,_}:>Plus[s]]&]],{n,15}] (* Gus Wiseman, May 16 2019 *)

def A169942(n):
    R = QQ['x']
    return sum(1 for c in cartesian_product([[0, 1]]*n) if max(R([1] + list(c) + [1])^2) == 2)
[A169942(n) for n in range(1,8)]
# Tomas Boothby, May 15 2012

a(n) = A169952(n) - A169952(n-1) for n>1. - Andrew Howroyd, Jul 09 2017

a(15)-a(30) from Nathaniel Johnston, Nov 12 2011

a(31)-a(50) from Tomas Boothby, May 15 2012

cp's OEIS Frontend

A129967 a(n) = A061909(n)^2.

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A129968 a(n) = sum of digits of A061909(n).

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A129969 a(n) = A061909(n) with digits reversed.

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A123977 Complement of A061909 (skinny numbers).

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A130596 Partial sums of skinny numbers (A061909).

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A159952 Skinny numbers (A061909) containing no 3's.

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A169939 Skinny numbers (A061909) containing no 2's.

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A224792 Smallest skinny number (A061909) with digit sum n.

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A069967 Duplicate of A061909.

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A169942 Number of Golomb rulers of length n.

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