A029523
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 6 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 5, 19, 35, 55, 85, 505, 12047, 113935, 1107173
Offset: 1
-
b = 6; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments from Larry Reeves (larryr(AT)acm.org), May 25 2001
a(8)-a(9) from Larry Reeves (larryr(AT)acm.org), Jun 11 2001
A029524
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 7 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 3, 9, 12, 36, 96, 128, 2267, 4031, 29416, 551444, 2033727, 2056797, 2477144, 7974180, 9482385
Offset: 1
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b = 7; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002; Aug 25 2002
A029525
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 8 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 7, 51, 63, 119, 3717, 91153, 147037, 208747, 2707075, 3097013
Offset: 1
-
b = 8; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
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lista(nn, m=8) = my(c, s, t); for(k=1, nn, t+=m^c*s=fromdigits(Vecrev(digits(k, m)), m); c+=logint(s, m)+1; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), Jun 04 2001
A029526
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 9 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 13, 16, 224, 320, 355, 800, 7856, 8720, 11683, 18829, 36464, 42544, 159125
Offset: 1
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b = 9; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
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lista(nn, m=9) = my(c, s, t); for(k=1, nn, t+=m^c*s=fromdigits(Vecrev(digits(k, m)), m); c+=logint(s, m)+1; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), May 25 2001
A029527
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 10 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 3, 9, 27, 99, 471, 60237, 1028301, 1085427, 2851947
Offset: 1
-
b = 10; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
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lista(nn, m=10) = my(c, s, t); for(k=1, nn, t+=m^c*s=fromdigits(Vecrev(digits(k, m)), m); c+=logint(s, m)+1; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments from Larry Reeves (larryr(AT)acm.org), May 25 2001. a(7) from Larry Reeves (larryr(AT)acm.org) Jan 14 2002
A029528
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 11 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 5, 20, 32, 815, 1325, 5600, 7889, 34385, 138724, 897165, 1409360, 2039049, 2182992, 9174075
Offset: 1
-
b = 11; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
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lista(nn, m=11) = my(c, s, t); for(k=1, nn, t+=m^c*s=fromdigits(Vecrev(digits(k, m)), m); c+=logint(s, m)+1; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), May 25 2001
A029529
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 12 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 11, 143, 1771, 1931, 3223, 7409, 17017, 32417, 125477, 863203
Offset: 1
-
b = 12; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
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lista(nn, m=12) = my(c, s, t); for(k=1, nn, t+=m^c*s=fromdigits(Vecrev(digits(k, m)), m); c+=logint(s, m)+1; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), May 25 2001
A029530
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 13 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 3, 9, 24, 48, 80, 96, 184, 549, 1083, 1392, 1624, 5085, 15968, 16000, 17763, 144843, 156200, 695808, 854904, 1001808, 1960016, 2002776, 2961952
Offset: 1
-
b = 13; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
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lista(nn, m=13) = my(c, s, t); for(k=1, nn, t+=m^c*s=fromdigits(Vecrev(digits(k, m)), m); c+=logint(s, m)+1; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), May 25 2001
A029531
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 14 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 13, 55, 99, 167, 185, 195, 1921, 4979, 14859, 37605, 48005, 88569, 122223, 278403, 394433, 1979771, 2082769, 2352363, 7323381
Offset: 1
-
b = 14; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
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lista(nn, m=14) = my(c, s, t); for(k=1, nn, t+=m^c*s=fromdigits(Vecrev(digits(k, m)), m); c+=logint(s, m)+1; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), May 25 2001
A029532
Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 15 (most significant digit on right and removing all least significant zeros before concatenation).
Original entry on oeis.org
1, 7, 17, 28, 424, 889, 2041, 2056, 2569, 3667, 3988, 7553, 8351, 13349, 28304, 28484, 38161, 41531, 60071, 126511, 444164, 588913, 681079, 2083457, 4753388, 7801841
Offset: 1
-
b = 15; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002 and Aug 25 2002
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