Sequences which I have corrected in the OEIS

 

The OEIS is the best resource for integer sequences on the internet and is maintained and presided over by Neil Sloane with the assistance of an editorial panel of around 70 mathematicians and computer programmers. It currently contains around 200000 sequences, and those listed below are ones that ‘slipped through the net’ and which I corrected:

 

 

1.

A094540

Units digits of the perfect numbers – a(20) corrected.

 

 

 

2.

A014963

a(n) = 1 unless n is a prime or prime power, in which case a(n) = the prime in question - closed form in terms of the binomial coefficients corrected.

 

 

 

3.

A009177

Hypotenuses of more than one Pythagorean triangle - typo corrected.

 

 

 

4.

A129802

Possible bases for Pepin’s primality test for Fermat numbers - incorrect reference to elite primes removed.

 

 

 

5.

A024361

Number of primitive Pythagorean triangles with leg n - Incorrect comment (to the effect that the members of this sequence were also the number of ways in which n could be expressed as the difference of two coprime squares) removed

 

 

 

6.

A060544

Centered 9-gonal (or nonagonal) numbers. Every third triangular number, starting with a(1)=1. Closed form corrected to comply with sequence offset 1.

 

 

 

7.

A145397

Non tetrahedral numbers. Defining formula corrected.

 

 

 

8.

A002414

Octagonal pyramidal numbers: n(n+1)(2n-1)/2. Incorrect formula deleted.

 

 

 

9.

A073636

Digital root of n^3. The given fraction contained a spurious, leading 1 in its decimal expansion. Replaced with the correct fraction.

 

 

 

10.

A016791

(3n+2)^3. First digital root given in the proof in the comment line corrected.

 

 

 

11.

A113708

Limit set for operation of repeatedly replacing a number by the sum of the 4th power of its digits. Erroneous comment regarding the trajectory terminating conditions corrected. Also, added a zero to the set of least k’s which return a(n) for consistency with the first term of the given limit set. Similarly for the number of iterations required to get there, whilst also taking the opportunity to correct two of the existing terms.

 

 

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