A279431 -id:A279431 - cp's OEIS frontend

A279430 Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 0.

0, 2, 4, 5, 8, 9, 10, 16, 17, 18, 19, 22, 32, 33, 34, 35, 36, 37, 40, 41, 44, 64, 65, 66, 67, 68, 69, 70, 71, 76, 77, 80, 81, 84, 85, 87, 90, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 145, 146, 147, 151, 152, 153, 156, 157, 160, 161, 164

Offset: 1

Lars Blomberg, Jan 07 2017

Lars Blomberg, Table of n, a(n) for n = 1..10000
Andrew Weimholt, Middle digit in square numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A279431.

See A279420-A279429 for a base-10 version.

a[n_]:=Part[IntegerDigits[n,2],(Length[IntegerDigits[n,2]]+1)/2];
Select[Range[0,164],OddQ[Length[IntegerDigits[#^2,2]]] && a[#^2]==0 &] (* Indranil Ghosh, Mar 06 2017 *)
k2oQ[n_]:=Module[{idn=IntegerDigits[n^2,2],len},len=Length[idn];OddQ[ len] && idn[[(len+1)/2]]==0]; Select[Range[0,200],k2oQ] (* Harvey P. Dale, Jan 29 2020 *)

isok(k) = my(d=digits(k^2, 2)); (#d%2 == 1) && (d[#d\2 +1] == 0);
for(k=0, 164, if(k==0 || isok(k)==1, print1(k,", "))); \\ Indranil Ghosh, Mar 06 2017

i=0
j=1
while i<=164:
    n=str(bin(i**2)[2:])
    l=len(n)
    if l%2 and n[(l-1)//2]=="0":
        print(str(i), end=",")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A280640 Numbers k such that k^3 has an odd number of digits and the middle digit is 0.

Original entry on oeis.org

0, 30, 40, 42, 100, 101, 115, 116, 123, 126, 135, 163, 164, 171, 199, 200, 201, 214, 468, 479, 487, 498, 500, 502, 513, 520, 525, 543, 557, 562, 564, 575, 576, 577, 578, 579, 585, 596, 600, 615, 623, 642, 656, 661, 666, 690, 695, 697, 700, 705, 709, 717, 721

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 0, 27000, 64000, 74088, 1000000, 1030301, 1520875, 1560896, ...

			0^3 = (0), 126^3 = 200(0)376, 562^3 = 1775(0)4328.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280641-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

a[n_]:=Part[IntegerDigits[n], (Length[IntegerDigits[n]] + 1)/2];
Select[Range[0, 721], OddQ[Length[IntegerDigits[#^3]]] && a[#^3]==0 &] (* Indranil Ghosh, Mar 06 2017 *)

isok(k) = my(d=digits(k^3)); (#d%2 == 1) && (d[#d\2 +1] == 0);
for(k=0, 721, if(k==0 || isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017

i=0
j=1
while i<=721:
    n=str(i**3)
    l=len(n)
    if l%2 and n[(l-1)//2]=="0":
        print(str(i), end=",")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A280649 Numbers k such that k^3 has an odd number of digits and the middle digit is 9.

Original entry on oeis.org

28, 33, 41, 108, 132, 157, 159, 175, 178, 181, 184, 187, 190, 193, 196, 204, 207, 209, 466, 474, 480, 486, 492, 508, 514, 515, 518, 519, 528, 536, 539, 552, 570, 588, 611, 627, 638, 648, 651, 657, 658, 659, 660, 706, 707, 708, 714, 719, 745, 757, 763, 765, 772

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 21952, 35937, 68921, 1259712, 2299968, 3869893, 4019679, 5359375, ...

			28^3 = 21(9)52, 181^3 = 592(9)741, 536^3 = 1539(9)0656.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280648, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

ond9Q[n_]:=Module[{idn=IntegerDigits[n^3],len},len=Length[idn];OddQ[len]&&idn[[(len+1)/2]]==9]; Select[Range[800],ond9Q] (* Harvey P. Dale, Mar 14 2018 *)

A280641 Numbers k such that k^3 has an odd number of digits and the middle digit is 1.

Original entry on oeis.org

1, 6, 8, 23, 44, 45, 102, 106, 110, 114, 117, 121, 137, 148, 152, 153, 162, 168, 176, 185, 189, 194, 206, 210, 478, 488, 512, 533, 553, 560, 574, 580, 626, 639, 655, 662, 669, 671, 676, 682, 683, 684, 685, 693, 704, 710, 730, 731, 737, 742, 758, 761, 767, 771

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 1, 216, 512, 12167, 85184, 91125, 1061208, 1191016, ...

			1^3 = (1), 114^3 = 148(1)544, 560^3 = 1756(1)6000

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640, A280642-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

a[n_]:=Part[IntegerDigits[n], (Length[IntegerDigits[n]] + 1)/2];
Select[Range[0, 771], OddQ[Length[IntegerDigits[#^3]]] && a[#^3]==1 &] (* Indranil Ghosh, Mar 06 2017 *)

isok(k) = my(d=digits(k^3)); (#d%2 == 1) && (d[#d\2 +1] == 1);
for(k=0, 771, if(isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017

i=0
j=1
while i<=771:
    n=str(i**3)
    l=len(n)
    if l%2 and n[(l-1)//2]=="1":
        print(str(i), end=', ')
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A280642 Numbers k such that k^3 has an odd number of digits and the middle digit is 2.

Original entry on oeis.org

5, 9, 103, 113, 133, 146, 151, 154, 165, 180, 198, 202, 470, 473, 493, 496, 504, 507, 521, 531, 538, 542, 566, 569, 581, 591, 593, 599, 612, 618, 620, 650, 654, 673, 681, 686, 703, 711, 715, 728, 729, 732, 740, 779, 801, 829, 841, 850, 855, 856, 857, 858, 874

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 125, 729, 1092727, 1442897, 2352637, 3112136, 3442951, 3652264, ...

			5^3 = 1(2)5, 180^3 = 583(2)000, 618^3 = 2360(2)9032.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280641, A280643-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

a[n_]:=Part[IntegerDigits[n],(Length[IntegerDigits[n]]+1)/2];
Select[Range[0,874],OddQ[Length[IntegerDigits[#^3]]] && a[#^3]==2 &] (* Indranil Ghosh, Mar 06 2017 *)

isok(k) = my(d=digits(k^3)); (#d%2 == 1) && (d[#d\2 +1] == 2);
for(k=0, 874, if(isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017

i=0
j=1
while i<=874:
    n=str(i**3)
    l=len(n)
    if l%2 and n[(l-1)//2]=="2":
        print(str(i), end=', ')
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A280643 Numbers k such that k^3 has an odd number of digits and the middle digit is 3.

Original entry on oeis.org

29, 34, 39, 46, 118, 125, 141, 142, 155, 161, 170, 211, 213, 477, 489, 511, 522, 526, 529, 535, 554, 573, 582, 586, 589, 631, 632, 633, 645, 663, 680, 691, 699, 723, 733, 744, 747, 770, 785, 790, 816, 817, 832, 854, 859, 863, 869, 873, 878, 892, 897, 901, 923

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 24389, 39304, 59319, 97336, 1643032, 1953125, 2803221, 2863288, ...

			29^3 = 24(3)89, 161^3 = 417(3)281, 663^3 = 2914(3)4247.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280642, A280644-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

Select[Range[925],OddQ[len=Length[IntegerDigits[#^3]]]&&Part[IntegerDigits[#^3],(len+1)/2]==3 &] (* Stefano Spezia, Oct 03 2023 *)

A280644 Numbers k such that k^3 has an odd number of digits and the middle digit is 4.

Original entry on oeis.org

7, 104, 112, 140, 143, 158, 166, 186, 188, 195, 465, 467, 490, 541, 558, 572, 595, 598, 604, 605, 606, 607, 613, 616, 622, 625, 630, 634, 635, 640, 643, 647, 653, 667, 675, 679, 687, 702, 712, 718, 720, 727, 734, 738, 759, 764, 783, 787, 802, 810, 815, 818

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 343, 1124864, 1404928, 2744000, 2924207, 3944312, 4574296, 6434856, ...

			7^3 = 3(4)3, 195^3 = 741(4)875, 640^3 = 2621(4)4000

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280643, A280645-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

Select[Range[1000],OddQ[IntegerLength[#^3]]&&NumberDigit[#^3,(IntegerLength[ #^3]-1)/2]==4&] (* Harvey P. Dale, Aug 12 2021 *)

A280645 Numbers k such that k^3 has an odd number of digits and the middle digit is 5.

Original entry on oeis.org

26, 43, 107, 109, 119, 122, 136, 139, 144, 150, 177, 179, 197, 203, 205, 472, 476, 494, 499, 501, 506, 510, 523, 537, 555, 561, 563, 568, 583, 603, 608, 629, 636, 649, 664, 694, 696, 726, 752, 753, 762, 766, 769, 780, 795, 796, 807, 814, 819, 826, 831, 845

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 17576, 79507, 1225043, 1295029, 1685159, 1815848, 2515456, 2685619, ...

			26^3 = 17(5)76, 150^3 = 337(5)000, 603^3 = 2192(5)6227

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280644, A280646-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

Select[Range[900],OddQ[IntegerLength[#^3]]&&IntegerDigits[#^3][[(IntegerLength[ #^3]+1)/2]]==5&] (* Harvey P. Dale, Aug 24 2017 *)

A280646 Numbers k such that k^3 has an odd number of digits and the middle digit is 6.

Original entry on oeis.org

22, 25, 27, 36, 37, 124, 129, 134, 147, 156, 160, 169, 469, 497, 503, 527, 532, 540, 547, 548, 549, 565, 571, 587, 602, 609, 652, 670, 672, 678, 688, 698, 713, 716, 722, 735, 741, 746, 751, 754, 755, 789, 794, 797, 798, 805, 813, 820, 828, 849, 866, 883, 887

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 10648, 15625, 19683, 46656, 50653, 1906624, 2146689, 2406104, ...

			22^3 = 10(6)48, 156^3 = 379(6)416, 678^3 = 3116(6)5752.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280645, A280647-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

Select[Range[887], OddQ[len=Length[IntegerDigits[#^3]]]&&Part[IntegerDigits[#^3], (len+1)/2]==6 &] (* Stefano Spezia, Oct 03 2023 *)

A280647 Numbers k such that k^3 has an odd number of digits and the middle digit is 7.

Original entry on oeis.org

31, 32, 105, 111, 128, 130, 149, 167, 173, 191, 192, 475, 483, 484, 491, 509, 524, 530, 534, 545, 546, 550, 556, 559, 584, 590, 592, 597, 614, 619, 624, 628, 637, 641, 665, 668, 692, 701, 725, 743, 750, 760, 781, 793, 809, 824, 836, 837, 843, 852, 861, 864

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 29791, 32768, 1157625, 1367631, 2097152, 2197000, 3307949, 4657463, ...

			31^3 = 29(7)91, 191^3 = 696(7)871, 619^3 = 2371(7)6659.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280646, A280648-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

Select[Range[865], OddQ[len=Length[IntegerDigits[#^3]]]&&Part[IntegerDigits[#^3], (len+1)/2]==7 &] (* Stefano Spezia, Oct 03 2023 *)

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A279430 Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 0.

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A280640 Numbers k such that k^3 has an odd number of digits and the middle digit is 0.

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A280649 Numbers k such that k^3 has an odd number of digits and the middle digit is 9.

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A280641 Numbers k such that k^3 has an odd number of digits and the middle digit is 1.

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A280642 Numbers k such that k^3 has an odd number of digits and the middle digit is 2.

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A280643 Numbers k such that k^3 has an odd number of digits and the middle digit is 3.

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A280644 Numbers k such that k^3 has an odd number of digits and the middle digit is 4.

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A280645 Numbers k such that k^3 has an odd number of digits and the middle digit is 5.

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