A101039 Pythagorean years: a Pythagorean year is one whose digits partition into two disjoint sets such that, considering digital sums, the Pythagorean relation 5^2=4^2 + 3^2 is evinced.

799, 889, 898, 979, 988, 997, 1699, 1789, 1798, 1879, 1888, 1897, 1969, 1978, 1987, 1996, 2599, 2689, 2698, 2779, 2788, 2797, 2869, 2887, 2896, 2959, 2968, 2977, 2986, 2995, 3499, 3589, 3598, 3679, 3688, 3697, 3769, 3796, 3859, 3886, 3895, 3949, 3958

Offset

1,1

References

J. P. Boudine, La geometrie de la chambre a air, pp. 88-90 Vuibert Paris 1998.

Links

Table of n, a(n) for n=1..43.

Example

1699 and 1888, for instance, are in the sequence (as are all permutations of them) because we have 1+6+9+9=(1+6+9)+9 and (1+8)+(8+8)=1+8+8+8.
All ordered solutions for years through 9999 follow with corresponding additional permutations:
0799 -> {979,997,7099,7909,7990,9079,9097,9709,9790,9907,9970}
0889 -> {898,988,8089,8098,8809,8890,8908,8980,9088,9808,9880}
1699 -> {1969,1996,6199,6919,6991,9169,9196,9619,9691,9916,9961}
1789 -> {1798,1879,1897,1978,1987,7189,7198,7819,7891,7918,7981,...}
1888 -> {8188,8818,8881}
2599 -> {2959,2995,5299,5929,5992,9259,9295,9529,9592,9925,9952}
2689 -> {2698,2869,2896,2968,2986,6289,6298,6829,6892,6928,6982,...}
2779 -> {2797,2977,7279,7297,7729,7792,7927,7972,9277,9727,9772}
2788 -> {2878,2887,7288,7828,7882,8278,8287,8728,8782,8827,8872}
3499 -> {3949,3994,4399,4939,4993,9349,9394,9439,9493,9934,9943}
3589 -> {3598,3859,3895,3958,3985,5389,5398,5839,5893,5938,5983,...}
3679 -> {3697,3769,3796,3967,3976,6379,6397,6739,6793,6937,6973,...}
3688 -> {3868,3886,6388,6838,6883,8368,8386,8638,8683,8836,8863}
4489 -> {4498,4849,4894,4948,4984,8449,8494,8944,9448,9484,9844}
4579 -> {4597,4759,4795,4957,4975,5479,5497,5749,5794,5947,5974,...}
4588 -> {4858,4885,5488,5848,5884,8458,8485,8548,8584,8845,8854}
4669 -> {4696,4966,6469,6496,6649,6694,6946,6964,9466,9646,9664}
5569 -> {5596,5659,5695,5956,5965,6559,6595,6955,9556,9565,9655}

Crossrefs

Sequence in context: A256026 A200201 A045261 * A121642 A364087 A035886

Adjacent sequences: A101036 A101037 A101038 * A101040 A101041 A101042

Keyword

nonn,base

Author

Lekraj Beedassy, Jan 21 2005

Extensions

Extended by Ray Chandler, Jan 25 2005

Status

approved