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 11-17 of 17 results.

A282144 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 3.

Original entry on oeis.org

4, 8, 11, 12, 19, 24, 28, 33, 36, 40, 47, 52, 56, 57, 61, 68, 72, 80, 84, 85, 92, 97, 99, 104, 108, 109, 113, 120, 125, 141, 145, 156, 168, 170, 171, 172, 183, 193, 204, 208, 216, 218, 229, 240, 244, 245, 250, 252, 255, 257, 269, 276, 278, 280, 291, 297, 301, 312
Offset: 1

Views

Author

Paolo P. Lava, Giovanni Resta, Feb 07 2017

Keywords

Comments

All the palindromic numbers in base 3 with an even number of digits belong to the sequence.
Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.

Examples

			229 in base 3 is 22111. If we split the number in 22 and 111 we have 2*1 + 2*2 = 6 for the left side and 1*1 + 1*2 + 1*3 = 6 for the right one.

Links

Crossrefs

Cf. A282107 - A282115, A282143, A282145 - A282151.

Programs

  • Maple
    P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
for k from 1 to nops(a)-1 do
if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i,3),i=1..10^3);

A282145 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 4.

Original entry on oeis.org

5, 10, 15, 18, 20, 23, 33, 40, 53, 60, 65, 67, 72, 80, 85, 92, 98, 105, 118, 125, 130, 132, 137, 150, 157, 160, 163, 170, 183, 190, 193, 195, 202, 212, 215, 222, 235, 240, 255, 260, 261, 268, 274, 281, 288, 294, 301, 307, 314, 320, 321, 326, 333, 339, 340, 346
Offset: 1

Views

Author

Paolo P. Lava, Giovanni Resta, Feb 07 2017

Keywords

Comments

All the palindromic numbers in base 4 with an even number of digits belong to the sequence.
Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.

Examples

			222 in base 4 is 3132. If we split the number in 31 and 32 we have 1*1 + 3*2 = 7 for the left side and 3*1 + 2*2 = 7 for the right one.

Links

Crossrefs

Cf. A282107 - A282115, A282143, A282144, A282146 - A282151.

Programs

  • Maple
    P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
for k from 1 to nops(a)-1 do
if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i,4),i=1..10^3);

A282146 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 5.

Original entry on oeis.org

6, 12, 18, 24, 27, 30, 33, 39, 51, 54, 60, 81, 90, 102, 111, 120, 126, 128, 134, 135, 150, 156, 165, 177, 186, 195, 207, 216, 228, 237, 246, 252, 255, 261, 270, 282, 291, 300, 303, 312, 321, 333, 342, 354, 363, 372, 376, 378, 387, 396, 405, 408, 417, 429, 438, 447
Offset: 1

Views

Author

Paolo P. Lava, Giovanni Resta, Feb 07 2017

Keywords

Comments

All the palindromic numbers in base 5 with an even number of digits belong to the sequence.
Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
Numbers with this property in all the bases from 2 to 5 are: 3120, 9615, 10366, 16610, 17812, 22129, 33329, 100726, 163800, 202039, 208172, 212636, 258221, 270337, 298575, 420240, 462608, 475782, 492420, 523679, 549537, 550200, 587842, 594511, 610273, 655350, 671844, 675872, 681280, 730161, 738480, 840798, 842614, 848655, 855973, 925515, 987751, ...

Examples

			447 in base 5 is 3242. If we split the number in 32 and 42 we have 2*1 + 3*2 = 8 for the left side and 4*1 + 2*2 = 8 for the right one.

Links

Crossrefs

Cf. A282107 - A282115, A282143 - A282145, A282147 - A282151.

Programs

  • Maple
    P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
for k from 1 to nops(a)-1 do
if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i,5),i=1..10^3);

A282147 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 6.

Original entry on oeis.org

7, 14, 21, 28, 35, 38, 42, 45, 52, 59, 73, 76, 83, 84, 115, 126, 146, 157, 168, 188, 199, 210, 217, 219, 226, 228, 233, 252, 257, 259, 270, 290, 301, 312, 332, 343, 354, 363, 374, 385, 405, 416, 427, 434, 438, 445, 456, 476, 487, 498, 504, 507, 518, 529, 549, 560
Offset: 1

Views

Author

Paolo P. Lava, Giovanni Resta, Feb 07 2017

Keywords

Comments

All the palindromic numbers in base 6 with an even number of digits belong to the sequence.
Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
Numbers with this property in all the bases from 2 to 6 are:
420240, 610273, 848655, 855973, 987751, 1830038, 2347657, 3480366, 3519545, 4832865, 5141958, 6050107, 9010530, 9770426, 11520023, 13951022, 14036167, 14694080, 15106072, 16487203, 24125707, 25209012, ...

Examples

			580 in base 6 is 2404. If we split the number in 24 and 04 we have 4*1 + 2*2 = 8 for the left side and 0*1 + 4*2 = 8 for the right one.

Links

Crossrefs

Cf. A282107 - A282115, A282143 - A282146, A282148 - A282151.

Programs

  • Maple
    P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
for k from 1 to nops(a)-1 do
if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i,6),i=1..10^3);

A282148 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 7.

Original entry on oeis.org

8, 16, 24, 32, 40, 48, 51, 56, 59, 67, 75, 83, 99, 102, 110, 112, 118, 153, 155, 168, 198, 211, 224, 254, 267, 280, 297, 310, 323, 336, 344, 346, 354, 357, 362, 370, 392, 397, 400, 405, 413, 443, 456, 469, 499, 512, 525, 542, 555, 568, 581, 598, 611, 624, 641, 654
Offset: 1

Views

Author

Paolo P. Lava, Feb 15 2017

Keywords

Comments

All the palindromic numbers in base 7 with an even number of digits belong to the sequence.
Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
The first number with this property in all the bases from 2 to 7 is
86964945. - Giovanni Resta, Feb 15 2017

Examples

			641 in base 7 is 1604. If we split the number in 16 and 04 we have 6*1 + 1*2 = 8 for the left side and 0*1 + 4*2 = 8 for the right one.

Links

Crossrefs

Cf. A282107 - A282115, A282143 - A282147.

Programs

  • Maple
    P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
for k from 1 to nops(a)-1 do
if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i,7),i=1..10^3);

A282150 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 9.

Original entry on oeis.org

10, 20, 30, 40, 50, 60, 70, 80, 83, 90, 93, 103, 113, 123, 133, 143, 163, 166, 176, 180, 186, 196, 206, 249, 253, 259, 269, 270, 326, 332, 343, 360, 416, 433, 450, 489, 506, 523, 540, 579, 596, 613, 630, 652, 669, 686, 703, 720, 730, 732, 742, 747, 752, 762, 772
Offset: 1

Views

Author

Paolo P. Lava, Feb 15 2017

Keywords

Comments

All the palindromic numbers in base 9 with an even number of digits belong to the sequence.
Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
The first number with this property in all the bases from 2 to 9 is 1030854453981. - Giovanni Resta, Feb 16 2017

Examples

			762 in base 9 is 1036. If we split the number in 103 and 6 we have 3*1 + 0*2 + 1*3 = 6 for the left side and 6*1 = 6 for the right one.

Links

Crossrefs

Cf. A282107-A282115, A282143-A282149, A282151.

Programs

  • Maple
    P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
for k from 1 to nops(a)-1 do
if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i,9),i=1..10^3);

A282149 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 8.

Original entry on oeis.org

9, 18, 27, 36, 45, 54, 63, 66, 72, 75, 84, 93, 102, 111, 129, 132, 141, 144, 150, 159, 198, 201, 207, 216, 258, 273, 288, 330, 345, 360, 387, 402, 417, 432, 459, 474, 489, 504, 513, 515, 524, 528, 533, 542, 551, 576, 581, 585, 590, 599, 600, 642, 647, 657, 672
Offset: 1

Views

Author

Paolo P. Lava, Feb 15 2017

Keywords

Comments

All the palindromic numbers in base 8 with an even number of digits belong to the sequence.
Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
The first number with this property in all the bases from 2 to 8 is
10296444436. - Giovanni Resta, Feb 16 2017

Examples

			672 in base 8 is 1240. If we split the number in 12 and 40 we have 2*1 + 1*2 = 4 for the left side and 4*1 + 0*2 = 4 for the right one.

Links

Crossrefs

Cf. A282107 - A282115, A282143 - A282148, A282150, A282151.

Programs

  • Maple
    P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
for k from 1 to nops(a)-1 do
if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i,8),i=1..10^3);
Previous Showing 11-17 of 17 results.

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