Tag Archives: sequence

Division-multiplication parabolas, triplications, and quadratic residues

Introduction Many strands of our investigations on conic-generating integer sequences, word fractals and cellular automaton models for pattern formation came together in an unexpected manner while investigating a simple integer sequence. While some of these connections have have been known … Continue reading

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A note on the least prime divisor sequences of 2p plus or minus 1

Let be the sequence of prime numbers: 2, 3, 5, 7… Define the sequences such that . Then sequence is defined such that is the lowest prime divisor (LPD) of and sequence is defined so that is the LPD of … Continue reading

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A sequence related to prime counting

The current note arose as an exploration branching off from the matter discussed in these earlier notes: this one and this one. As we saw before, Carl Gauss, while still in his teens, produced his first estimate of the prime … Continue reading

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Some novel observations concerning quadratic roots and fractal sequences

Disclaimer: To our knowledge we have not found the material presented here laid out here presented in completeness elsewhere. However, we should state that we do not follow the mathematical literature as a professional and could have missed stuff. Introduction … Continue reading

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Triangles, Hexes and Cubes

One philosophical question which we have often ponder about is: Are numbers “real”? One way to approach this question is via figurate numbers, where numbers directly manifest as very tangible geometry. This idea has deep roots in our tradition: as … Continue reading

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Hofstadter and Nārāyaṇa: connections across space and time

The scientist-philosopher Douglas Hofstadter presents an interesting single-seeded sequence H in his book ‘Gödel, Escher, Bach: An Eternal Golden Braid’. It is generated by the recurrence relation, where …(1) Working it out one can see that it takes the form: … Continue reading

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