interesting integer sequences


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This paper gives a brief description of the author’s database of integer sequences, now over 35 years old, together with a selection of a few of the most interesting sequences in the table. Let me introduce you to the Ulam sequence. What I do know, however, is that there's a very nice link between the golden ratio and the Fibonacci sequence which explains the growth pattern of many things in nature. My Favorite Integer Sequences N. J. ���kc For more than 50 years, the mathematician Neil Sloane has curated the authoritative collection of interesting and important integer sequences. %PDF-1.2 x��\Y�7r�3�7��?X�N-�C�������w�Y���Z�R�տ��@��BsD��+P �痙�yyP�>(�o����;j��,�|��]���������fZs0�.��9^}����ѳ���Ju�?���KX>��4���O�2�˿����Ο~۟�=�y>h�XQ���uNK8�S�����Ӆ]�u>�cH�N���S���W'��L8�p�v�6����,*:�ߝ.��`M��oNvQZ9w��s�bɤ����Nj�����OV/ژ�CL.���P(���k������P:8~��h��D���'��؃Ӆ^R����W�˙�\���s�M�C^r0��_���pa�����L�&��;.� ��?? �~�4���9D{��׬�X۔�}i�n�P��x p�2�L�fɆ�¹�Ħ3�!�F�Ǫ\�Kw��l�Ұ$ Many unsolved problems are … As for your question, there are a ton of interesting sequences but I can't really think of anyone right now. Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elements in the sequence. <>
)p^�u�MrKF��I3]b)O�G|Kh(nВ]�܇: �~=��������5��|�4�}8�FG��$�=�me������ՉT� ���]2�G��7���,��r�Re���Q0�����>���",�X����_��~=��1�-y�������u0�AUcc�N��#6 ��5 A. Sloane Information Sciences Research AT&T Shannon Lab Florham Park, NJ 07932-0971 USA Email: njas@research.att.com Abstract.

]�E��G5nq��dzO�4^z�O�+�x�^`�F^�������ÇD�1&ٕL{H 3�Dd^��dOt�E��t~F�%M\p�W Neil Sloane is considered by some to be one of the most influential mathematicians of … Erica Klarreich. combinatorics Fibonacci numbers mathematics Q&A All topics. 5 0 obj Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as … %�쏢 August 6, 2015. Read Later. View PDF/Print Mode.

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et ApplicationsSome Remarks on Ballot-Type Sequences of Positive IntegersComputing Tournament Sequence Numbers efficiently with Matrix TechniquesIterated Absolute Values of Differences of Consecutive Primes "Integer Sequences Connected to the Laplace Continued Fraction and Ramanujan's Identity" (Abstract, pdf, ps, dvi, tex) Article 16.6.3: Mohamed Alaa and Mohammad Sadek, "On Geometric Progressions on Hyperelliptic Curves" (Abstract, pdf, ps, dvi, tex) Article 16.6.4: Andrew R. Booker, If you come across a number sequence and want to know if it has been studied before, there is only one place to look, the On-Line Encyclopedia of Integer Sequences (or OEIS). stream

The paper introduces and compares several of these classes of sequences, discussing recurrence relations, enumerative problems and questions concerning shortest sequences.

Increasing integer sequences and Goldbach's conjecture )✶�@�8�M8ON���x�nd�P@}�*�u��1B��FgE�C�T�_aI�&{��tC��{5�[0Ɇ(Ʈf�yp2i�چ㓾#�P�%�.�Z�ι���St ���%�P��O��`���d�ba�O���a���#�l����wE�M�щ�����j����"�R����Ġ\8�OX>���b��{���ǻ$8����`b"�'�8�j���:b��YG.h���i��M�o��3�x��q-��e�" ;�Caѧ����������=Ѫ�������-�y^#����[]�Ћ��L9u�X����O�E�9C�{3��f ���̊'L]p�`�uP�ʲ��C�Qi�T_�\i6��v�8��K���� �-v�:��! Contributing Correspondent. The idea behind it is very simple: start with some two positive integers, say [math]a_1 = 1[/math] and [math]a_2 = 2[/math]. This mathisfun page seems to explain it in a very geometric way.

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interesting integer sequences