Unification of Different Fields of Mathematics

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During WWII, André Weil proposed an idea for linking three fields of mathematics: number theory, geometry, and finite fields.

For the full story, please see the following link it Quanta Magazine's  article describing the unification of three major branches of mathematics: A Rosetta Stone of Mathematics. 

Also related, is the work begun by Robert Langlands, known as the Langlands program.

A371030 Contribution to the OEIS

 

A371030 n written in compositorial base. 0

0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 40, 41, 42, 43, 50, 51, 52, 53, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 123, 130, 131, 132, 133, 140, 141, 142, 143, 150, 151, 152, 153, 200, 201, 202, 203, 210, 211, 212, 213 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 0,3 COMMENTS Compositorial base is a mixed-radix representation using the composite numbers (A002808) from least to most significant. Places reading from right have values (1, 4, 24, 192, ...) = compositorial numbers (A036691). a(n) = concatenation of decimal digits of n in compositorial base. This concatenated representation is unsatisfactory for large n (above 172799), when coefficients of 10 or greater start to appear. LINKS Table of n, a(n) for n=0..55. EXAMPLE a(35)=123; 35 = 1*24 + 2*4 + 3*1. MATHEMATICA Table[FromDigits@ IntegerDigits[n, MixedRadix[Reverse@ ResourceFunction["Composite"]@ Range@ 8]], {n, 0, 55}] CROSSREFS Cf. A002808, A036691, A049345. Sequence in context: A301382 A288657 A055655 * A276326 A007090 A102859 Adjacent sequences: A371027 A371028 A371029 * A371031 A371032 A371033 KEYWORD nonn,base,less AUTHOR James C. McMahon, Mar 08 2024 STATUS approved

A370831 Contribution to the OEIS

 

A370831 Alternating sum of composites. 0

4, 2, 6, 3, 7, 5, 9, 6, 10, 8, 12, 9, 13, 11, 14, 12, 15, 13, 17, 15, 18, 16, 19, 17, 21, 18, 22, 20, 24, 21, 25, 23, 26, 24, 27, 25, 29, 26, 30, 27, 31, 29, 33, 30, 34, 31, 35, 33, 36, 34, 38, 36, 39, 37, 40, 38, 42, 39, 43, 41, 44, 42, 45, 43, 47, 44, 48, 45, 49, 46 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 1,1 COMMENTS Unlike equivalent sequence for primes, A008347, there are repeated terms. LINKS Table of n, a(n) for n=1..70. FORMULA a(n) = A002808(n) - a(n-1), for n>1. EXAMPLE a(4) = 9 - 8 + 6 - 4 = 3. MATHEMATICA Join[{4}, a[1]=4; a[n_]:=ResourceFunction["Composite"][n] - a[n-1]; Table[a[n], {n, 2, 70}]] (* or with signs *) R=70; a[1]=4; a[n_]:=a[n-1]-ResourceFunction["Composite"][n] *(-1)^n; Table[a[n], {n, 70}] CROSSREFS Cf. A002808, A008347. Sequence in context: A246879 A302794 A247361 * A297307 A163238 A097362 Adjacent sequences: A370827 A370828 A370830 * A370832 A370833 A370834 KEYWORD nonn AUTHOR James C. McMahon, Mar 02 2024 STATUS approved