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.

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A177083 A006093(k)-fold repetition of A001248(k), k=1,2,3,..

Original entry on oeis.org

4, 9, 9, 25, 25, 25, 25, 49, 49, 49, 49, 49, 49, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 169, 169, 169, 169, 169, 169, 169, 169, 169, 169, 169, 169
Offset: 1

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Author

Paul Curtz, Dec 09 2010

Keywords

Comments

Consider the initial terms of numerator sequences (dropping initial zeros) of
3; A005563=N(1) ,
5,3; A061037=N(2) ,
7,16,1; A061039=N(3) ,
9,5,33,3; A061041=N(4) ,
11,24,39,56,3; A061043=N(5) ,
13,7,5,4,85,1; A061045=N(6) ,
15,32,51,72,95,120,3; A061047=N(7) ,
17,9,57,5,105,33,161,3; A061049=N(8) ,
19,40,7,88,115,16,175,208,1; N(9),
21,11,69,6,1,39,189,14,261,3; N(10),
23,48,75,104,135,168,203,240,279,320,3; N(11)
One must add the following associated (minimum) squares (taken from squared entries in A172038) to these values to reach the next possible square not larger than the entry itself:
1; N(1)
4,1; N(2)
9,9,0; N(3)
16,4,16,1; N(4)
25,25,25,25,1; N(5)
36,9,4,0,36,0; N(6)
49,49,49,49,49,49,1; N(7)
64,16,64,4,64,16,64,1, ; N(8)
Only if the index of N(.) is a prime we obtain a string of equal consecutive terms in these complementary rows: 4, 9, 25, 49, 121, 169..
The current sequence lists the consecutive complementary squares, A001248, in the rows with prime index, including their multiplicity (which is A006093).
This generates a link between the primes and the Rydberg-Ritz spectrum of the hydrogen atom.

Crossrefs

Cf. A072055, A135177.
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