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.

User: J. Volkmar Schmidt

J. Volkmar Schmidt's wiki page.

J. Volkmar Schmidt has authored 3 sequences.

A366831 Self-locating strings within Pi: numbers n such that the reverse string n starts at position n in the decimal digits of Pi, where leading 3 is omitted.

Original entry on oeis.org

1, 50, 576, 242424, 746074, 10311073, 54848721, 103849853, 48438192357
Offset: 1

Author

J. Volkmar Schmidt, Oct 31 2023

Keywords

Examples

			50 is a term because '05' starts at position 50,
576 is a term because '675' starts at position 576:
Position        1 2 3 ... 50 51 ... 576 577 578 ...
Pi (3 omitted)  1 4 1 ... 0  5  ... 6   7   5   ...
		

Crossrefs

A366830 Self-locating strings within Pi: numbers n such that the reverse string n starts at position n in the decimal digits of Pi, where 3 is the first digit.

Original entry on oeis.org

5, 1610, 5833, 82699856, 9633661255, 17292288245, 78246420246
Offset: 1

Author

J. Volkmar Schmidt, Oct 31 2023

Keywords

Examples

			1610 is a term because '0161' starts at position 1610:
Position  1  2  3  4  ...  1610  1611  1612  1613  ...
Pi        3  1  4  1  ...    0     1     6     1   ...
		

Crossrefs

A366829 Number of 9-step self-avoiding king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 784, 436984, 3908376, 13530576, 30543072, 54738536, 85743256, 123447704, 167851880, 218955784, 276759416, 341262776, 412465864, 490368680, 574971224, 666273496, 764275496, 868977224, 980378680, 1098479864, 1223280776, 1354781416, 1492981784, 1637881880
Offset: 1

Author

J. Volkmar Schmidt, Oct 25 2023

Keywords

Comments

Proof of the formula follows proof scheme from David A. Corneth for A186864.
Distribution matrix of surrounding rectangles for 9-step walks is:
[0 0 0 0 0 0 0 0 2]
[0 0 0 0 3584 10496 10752 5120 1020]
[0 0 784 43856 129100 136320 83208 29160 4680]
[0 0 43856 258424 318816 215096 99984 29680 4296]
[0 3584 129100 318816 262816 142888 57376 15400 2100]
[0 10496 136320 215096 142888 67688 24288 5960 768]
[0 10752 83208 99984 57376 24288 7864 1760 212]
[0 5120 29160 29680 15400 5960 1760 360 40]
[2 1020 4680 4296 2100 768 212 40 4]

Examples

			Some solutions for 3 X 3:
  1 2 3  1 2 3  1 2 3  1 2 3  1 7 8  1 2 8
  4 5 6  6 5 4  8 9 4  7 6 4  6 2 9  3 7 9
  7 8 9  7 8 9  7 6 5  8 9 5  5 4 3  4 5 6
		

Crossrefs

Row 9 of A186861.

Formula

a(n) = 3349864*n^2 - 25942968*n + 47890984 for n>7.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 10. - Stefano Spezia, Oct 28 2023