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.

Showing 1-5 of 5 results.

A171775 a(n) = smallest number M such that there exist bases b_2, b_3, ..., b_n with the property that M written in base b_k is a k-digit palindrome for all k=2..n.

Original entry on oeis.org

1, 3, 5, 52, 130, 1885, 1073741824, 4398046511104
Offset: 1

Views

Author

James G. Merickel, Dec 18 2009

Keywords

Comments

a(n) is no more than 2^[(n-1)*(n-2)] for n > 6 (and equals it for n = 7 and 8 at least). The reason for this bound is that for this number for each length from n down to 3 there is at least one power of 2, 2^k, such that in base b = 2^k-1 the binomial expansion of (b+1)^floor([(n-1)*(n-2)]/k) multiplied by the remaining small power of 2 gives a palindromic expression not requiring carries in base b. James G. Merickel, Aug 05 2015

Examples

			a(6)=1885: the bases are 1884 (1885 is 11 in base 1884), 14 (1885 is 989 in base 14), 12 (it is 1111 in base 12), 6 (it is 12421 in base 6), and 4 (it is 131131 in base 4).

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A099165, A087155, A171701, A171702, A171703, A171704, A171705, A171706, A171740, A171741, A171742, A253294.

Extensions

a(7) and a(8) added by James G. Merickel, Feb 04 2010
Offset changed to 1, with corresponding addition of a(1) by James G. Merickel, Jul 24 2015
Comment corrected and explained.James G. Merickel, Aug 05 2015
Definition and example rewritten by N. J. A. Sloane, Aug 05 2015

A253290 Number of (n+1)X(2+1) 0..2 arrays with every 2X2 subblock sum differing from its neighbors horizontally, vertically, diagonally and antidiagonally.

Original entry on oeis.org

558, 3600, 23546, 167832, 1184928, 8243488, 57474376, 402165016, 2811886280, 19648735840, 137308874176, 959744819720, 6708131042848, 46884212361800, 327678437410752, 2290232105294136, 16007076725008072, 111877100758327680
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2014

Keywords

Comments

Column 2 of A253294

Examples

			Some solutions for n=4
..0..1..1....0..0..1....1..0..0....0..0..1....1..0..0....1..2..0....1..2..1
..0..0..2....0..0..2....1..0..0....1..2..2....0..1..0....2..2..1....0..2..2
..0..0..1....1..0..0....1..1..0....1..2..2....1..1..2....0..0..0....0..0..2
..0..2..1....0..2..2....0..2..2....0..1..0....1..2..1....0..1..1....0..1..0
..0..1..2....0..0..2....2..2..1....0..1..1....0..0..1....2..0..2....2..1..0

Links

Formula

Empirical: a(n) = 4*a(n-1) +22*a(n-2) -47*a(n-3) +847*a(n-4) -2548*a(n-5) -14241*a(n-6) +46156*a(n-7) -235684*a(n-8) +513456*a(n-9) +3142562*a(n-10) -12248092*a(n-11) +34872668*a(n-12) -44225096*a(n-13) -327631492*a(n-14) +1356943312*a(n-15) -3049192352*a(n-16) +2235968632*a(n-17) +17503809584*a(n-18) -67675653456*a(n-19) +140372058144*a(n-20) -119547407360*a(n-21) -386660564160*a(n-22) +1410208318912*a(n-23) -2855898321408*a(n-24) +4453728916224*a(n-25) -381216535552*a(n-26) -12897724549120*a(n-27) +35949674973184*a(n-28) -73144228077568*a(n-29) +67153529954304*a(n-30) +54469989974016*a(n-31) -290876893462528*a(n-32) +505744121200640*a(n-33) -360592985554944*a(n-34) -244530708480000*a(n-35) +1126160419258368*a(n-36) -1315197520183296*a(n-37) -66806203023360*a(n-38) +1063245997670400*a(n-39) -489223618560000*a(n-40)

A253291 Number of (n+1)X(3+1) 0..2 arrays with every 2X2 subblock sum differing from its neighbors horizontally, vertically, diagonally and antidiagonally.

Original entry on oeis.org

3844, 23546, 140536, 1029888, 7431136, 52784020, 376392916, 2705942488, 19441124904, 139538118106, 1001630063642, 7192898044676, 51663362450690, 371000801080586, 2664302414067690, 19133126021242278, 137412998986250836
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2014

Keywords

Comments

Column 3 of A253294

Examples

			Some solutions for n=3
..0..1..0..0....1..2..2..2....1..0..1..0....0..0..0..0....1..0..1..2
..0..0..1..2....0..0..0..1....2..0..0..2....1..2..0..0....2..0..1..2
..2..1..2..1....0..0..1..0....2..0..0..2....2..2..1..0....2..0..0..2
..1..2..0..0....1..2..1..1....2..1..2..2....2..2..1..1....0..0..0..1

Links

A253292 Number of (n+1)X(4+1) 0..2 arrays with every 2X2 subblock sum differing from its neighbors horizontally, vertically, diagonally and antidiagonally.

Original entry on oeis.org

26784, 167832, 1029888, 8153960, 61286116, 465921688, 3524494796, 26879615668, 204459584768, 1560668372324, 11882769388376, 90517446353584, 689680753666852, 5257319067276484, 40057456786744360, 305206750112569024
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2014

Keywords

Comments

Column 4 of A253294

Examples

			Some solutions for n=2
..1..0..0..0..0....0..2..2..2..2....1..2..0..0..1....0..1..2..2..2
..0..0..0..2..2....0..2..2..1..1....2..1..0..1..1....1..1..2..2..0
..1..2..2..1..1....1..0..2..0..2....2..2..1..0..2....2..1..0..1..0

Links

A253293 Number of (n+1)X(5+1) 0..2 arrays with every 2X2 subblock sum differing from its neighbors horizontally, vertically, diagonally and antidiagonally.

Original entry on oeis.org

186624, 1184928, 7431136, 61286116, 486417836, 4028778100, 32585471254, 268974784168, 2194325404780, 18267942030516, 149525306842164, 1236309598259424, 10153736125504116, 84093032702185292, 691354236502296106
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2014

Keywords

Comments

Column 5 of A253294

Examples

			Some solutions for n=1
..0..2..2..2..1..1....0..0..1..1..2..2....0..2..1..1..1..1....0..2..1..0..0..0
..1..1..1..2..0..1....2..0..0..2..2..0....0..2..1..0..0..1....2..1..0..2..0..0

Links

Showing 1-5 of 5 results.

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