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# User:Charles R Greathouse IV/Favorites

Of course no collection of "favorite" sequences can be canonical, or exhaustive, but these sequences are some that struck me as especially nice and which I wanted to record for future reference. You may enjoy them too!

## By author

This is a collection of some of my favorite sequences from these authors. Tastes vary, but I think these are nice.

• A Joerg Arndt: A065428, Numbers n such that no ${\displaystyle \scriptstyle x^{2}{\pmod {n}}}$ are prime.
• B Roger L. Bagula: A167660, Chocolate dove bar numerator: ${\displaystyle \scriptstyle a(n)\,=\,\sum _{k=0}^{\lfloor n/2\rfloor }k{n+k \choose k}{n \choose n-2k}+\sum _{k=0}^{\lceil n/2\rceil }k{n+k-1 \choose k-1}{n \choose n-2k+1}.}$
• John Michael Bergot: A154598, a(n) = smallest prime p such that p-1 and p+1 both have n prime factors.
• C Pierre CAMI: A115563, Decimal expansion of ${\displaystyle \scriptstyle \sum _{n\,>\,1}1/(n\log ^{2}n).}$
• Eric Chen: A253236, The unique prime p <= n such that n-th cyclotomic polynomial has a root mod p, or 0 if no such p exists.
• Marius Coman A214305, Fermat pseudoprimes to base 2 with two prime factors.
• Paul Curtz: A172412, Multiples of 4 with the property that addition of a square gives a square that is not larger than the square for any later term.
• E Jason Earls: A050150, Odd numbers with prime number of divisors.
• Rémi Eismann: A117078, a(n) = smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists.
• Labos Elemer: A082885, Primes followed by a larger-than-average prime gap.
• F Odimar Fabeny: A101402, a(0)=0, a(1)=1; for n>=2, let k = smallest power of 2 that is >= n, then a(n) = a(k/2) + a(n-1-k/2).
• G Gerasimov Sergey: pseudonym of Juri-Stepan Gerasimov
• Sergey Gerasimov: pseudonym of Juri-Stepan Gerasimov
• Irina Gerasimova: pseudonym of Juri-Stepan Gerasimov
• Juri-Stepan Gerasimov: A166955, ${\displaystyle \scriptstyle \phi (n)}$ is a perfect power.
• Charles R Greathouse IV: A173419, Length of shortest computation yielding n using addition, subtraction and multiplication.
• Ilya Gutkovskiy: A263653, a(n) = ${\displaystyle \scriptstyle \Omega (n)^{\omega (n)}.}$
• H Enoch Haga: A046731, Sum of primes < 10^n.
• Michael Joseph Halm: A081357, Sublime numbers, numbers for which the number of divisors and the sum of the divisors are both perfect.
• Syed Iddi Hasan: A215966, Number of ways prime(n) can be expressed as the sum of distinct smaller noncomposites.
• J. W. Helkenberg: A181732, Numbers n such that 90n + 1 is prime.
• K Agaram Kandadai Devaraj: A162290, the Pomerance index of the n-th 3-Carmichael number.
• Clark Kimberling: A025527, ${\displaystyle \scriptstyle n!/\operatorname {LCM} \{1,2,\ldots ,n\}}$
• L Michel Nicole Lagneau: A206709, Number of primes of the form ${\displaystyle \scriptstyle b^{2}+1}$ for ${\displaystyle \scriptstyle b\leq 10^{n}.}$
• Ilya Lopatin: pseudonym of Juri-Stepan Gerasimov
• Moshe Levin: A199692, Subsequence of Pythagorean primes (A002144): each square is used only once.
• Vincenzo Librandi: A172028, a(1) = 2; for n > 1, a(n) = smallest k such that a(n-1)^3+k is a cube.
• M James G. Merickel: A171810, The least k>0 such that ${\displaystyle \scriptstyle kx^{n}+\sum _{i=0}^{n-1}a(i)x^{i}}$ is irreducible.
• N Naohiro Nomoto: A058377, Number of solutions to ${\displaystyle \scriptstyle 1\pm 2\pm 3\pm \cdots \pm n=0.}$
• Thomas Nordhaus: A079296, Primes listed in order of their Andrica ranking.
• O Vladimir Orlovsky: A154293, Integers of the form t/6, where t = A000217(m) is a triangular number.
• P Omar Evaristo Pol: A161914, Gaps between the nontrivial zeros of Riemann zeta function, rounded to nearest integers, with a(1)=14.
• Jonathan Vos Post: A100200, Decimal Gödelization of antitheorems from propositional calculus, in Richard Schroeppel's metatheory of A101273.
• Ki Punches: A161002, Least prime of three consecutive primes (p1,p2,p3) such that p2-p1 and p3-p2 are both perfect squares.
• R Viswanathan Raman: A216503, a(n) = number of positive integers k such that ${\displaystyle \scriptstyle n\,=\,x^{2}+ky^{2}}$ has a solution with x>0, y>0.
• Alena Rittina: pseudonym of Juri-Stepan Gerasimov
• Felice Russo: A045917, From Goldbach problem: number of decompositions of 2n into unordered sums of two primes.
• S Nadezda Sokirka: pseudonym of Juri-Stepan Gerasimov
• Michael Somos: A186704, the minimum number of distinct distances determined by n points in the Euclidean plane.
• Carmine Suriano: A178576, Primes that are the sum of two Fibonacci numbers.
• T Giovanni Teofilatto: A123193, Natural numbers with number of divisors equal to a Fibonacci number.
• W Arkadiusz Wesolowski: A180247, Prime Brier numbers: prime n such that for all k >= 1 the numbers n*2^k + 1 and n*2^k - 1 are composite.
• David W. Wilson: A023193, Largest number of pairwise coprime numbers that can occur in an interval of length n.
• Z Eva-Maria Zschorn: A172271, Smaller member p of a twin prime pair (p,p+2) with a cube sum N^3.

If your name's not here, don't worry; there are thousands of authors on the OEIS and I haven't included choices for them all. Still, I may expand the list as time permits.

If you would like to be included, please leave a note on my Talk page or send me (charles (at) my website, crg4.com) an email with your best half-dozen sequences. I can't promise I'll get to it quickly, and of course our tastes may not match.

## By keyword

This is a collection of some of my favorite sequences with these keywords. Nonmathematical sequences are traditionally marked "dumb", but that doesn't mean they aren't interesting, for example.

• base: A005349, Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits.
• dumb: A215009, Numbers which are "easy" to key on a computer numpad.