The Newest Boring Number: 20990

In a prior post, 20067 was described as a "boring" number. It was considered boring because it was the lowest number not occurring in the On-Line Encyclopedia of Integer Sequences (OEIS). 

However, this month, a new OEIS sequence was published, including 20667 as a term. The sequence is: A379570 - OEIS. 20667 is the fifth sequence term defined by "Number of n-digit numbers that have exactly 8 divisors."

So now, the lowest number not occurring in the OEIS is: 20990.

Update 1/2/2025. Just after 20067 was replaced by a new most boring number, a sequence that included the prime number 45247 was submitted, so it lost its designation as the most boring prime number. Now, the lowest prime number not occurring in the OEIS is 48973 (the 5033rd prime).

The new sequence including 45247 is: A379615 Numerators of the partial sums of the reciprocals of the sum of bi-unitary divisors function (A188999).

Update June 25, 2026: The following site tracks the top most "unintereseting" numbers: manman4 | OEIS Uninteresting Numbers and Sloane's Gap

A378384 Contribution to the OEIS

 A378384

Digital root of the sum of the previous 3 terms; a(0) = a(1) = a(2) = 1.

0

1, 1, 1, 3, 5, 9, 8, 4, 3, 6, 4, 4, 5, 4, 4, 4, 3, 2, 9, 5, 7, 3, 6, 7, 7, 2, 7, 7, 7, 3, 8, 9, 2, 1, 3, 6, 1, 1, 8, 1, 1, 1, 3, 5, 9, 8, 4, 3, 6, 4, 4, 5, 4, 4, 4, 3, 2, 9, 5, 7, 3, 6, 7, 7, 2, 7, 7, 7, 3, 8, 9, 2, 1, 3, 6, 1, 1, 8, 1, 1, 1, 3, 5, 9, 8, 4, 3, 6

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

This differs from A112661 which is sum of digits of sum of previous 3 terms.

Digital root of A000213 (tribonacci numbers beginning {1,1,1}).

This has a period of 39 beginning with the first term.

Decimal expansion of 12373315960504936995263080863765792902/111111111111111111111111111111111111111 = 0.[111359843644544432957367727773892136118] (periodic).

LINKS

Table of n, a(n) for n=0..87.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

FORMULA

a(n) = A010888(A000213(n)).

MATHEMATICA

Nest[Append[#, ResourceFunction["AdditiveDigitalRoot"][Total[Take[#, -3]]]]&, {1, 1, 1}, 85]

CROSSREFS

Cf. A000213, A010888, A112661.

Sequence in context: A221967 A079428 A094548 * A112661 A230725 A254689

Adjacent sequences: A378381 A378382 A378383 * A378386 A378388 A378389

KEYWORD

nonn,base,easy,new

AUTHOR

James C. McMahon, Nov 24 2024

STATUS

approved

Primes that can be expressed in the form p² + 4q², where both p and q are prime numbers

In a significant advancement for number theory, mathematicians Ben Green of the University of Oxford and Mehtaab Sawhney of Columbia University have introduced a novel method for identifying specific types of prime numbers. Their work, detailed in a recent Quanta Magazine article, focuses on primes that can be expressed in the form p² + 4q², where both p and q are prime numbers.

Quanta Magazine

Prime numbers, defined as numbers greater than 1 that have no positive divisors other than 1 and themselves, are fundamental to mathematics. Understanding their distribution has been a longstanding challenge. While the infinitude of primes was established by Euclid around 300 BCE, identifying primes that satisfy additional constraints has proven difficult. Green and Sawhney's achievement in proving the existence of infinitely many primes of the form p² + 4q² represents a significant breakthrough in this area.

Their approach diverged from traditional methods by incorporating tools from other mathematical disciplines, demonstrating the potential for interdisciplinary techniques to address complex problems in number theory. This innovative strategy not only resolved a specific conjecture but also opened avenues for applying similar methods to other mathematical challenges.

The implications of this discovery extend beyond the immediate result. By enhancing our understanding of prime distribution, it contributes to the broader field of analytic number theory and may influence related areas such as cryptography, where prime numbers play a crucial role.

For a more comprehensive exploration of Green and Sawhney's work and its significance, the full article is available on Quanta Magazine's website.

Quanta Magazine