* unitary nontotient numbers (cf. A047994, A005277, A135347)
* a(0)=0, a(1)=1, for n>1, a(n)=sigma(a(n-1))-a(n-1) if it is currently not in this sequence, otherwise a(n)=the smallest number currently not in this sequence
* Square array: A(m,n) is the number of cycles of the Kapakar maps of n-digit base m numbers.
* Square array: A(m,n) is the smallest number whose nth power is the sum of m positive nth powers (or 0 if no such number exists).
* Square array: A(m,n) is the smallest k>=1 such that (m*n^k+1)/gcd(m+1,n-1) is prime.
* Square array: A(m,n) is the smallest k>=1 such that (m*n^k-1)/gcd(m-1,n-1) is prime.
* Triangle: A(m,n) is the smallest odd prime p such that (m*p+n^p)/(m+n) is also prime.
* If n = 10*m+d with 0<=d<=9, a(n) = largest k such that m^k does not contain the digit d (or -1 if no such k exists).
* Numbers k such that 2*12^k-1 is prime.
* Smallest k such that 12*n^k+1 is prime.
* Smallest k such that (n-1)*n^k-1 is prime (Williams prime).
* Smallest k such that ((2n)^k-1)^2-2 is prime (Carol prime).
* Smallest k such that ((2n)^k+1)^2-2 is prime (Kynea prime).
* Biunique primes in base 2.
* Triunique primes in base 2.
* Smallest prime which is the concatenation of first k numbers in base n for some k.
* Smallest k such that the concatenate next digit at right hand end in base n (where the next digit after n-1 is again 0) is prime.
* Smallest Euler pseudoprime base n.
* Smallest n-Fibonacci U-pseudoprime. (323, 35, 119, 9, 9, 143, 25, 33, 9, 15, 123, 35, 9, 9, 15, 129, 51, 9, 33, 15, ...) (CF A081264 for n=1)
* Smallest n-Fibonacci V-pseudoprime. (CF A005845 for n=1)
* Smallest solution of z of x^3+y^3=n*z^3 which x,y,z>0, x!=y (0 if no solution exists).
* Smallest solution of z of x^4+y^4=n*z^4 which x,y,z>0, x!=y (0 if no solution exists).
* (Numerator and de.. of) Smallest solution of z of x^2+y^2=z^2 and xy/2=n.
* Smallest solution of (x,y,z) such that x^3+y^3+z^3=n such that ... (0 if no solution exists).
* (minimal primes, weakly primes, emirps, ...) in base b (for: b=2, b=3, ..., b=16).
* quasi-minimal primes in base b (for b=2, b=3, ..., b=16). (also number of such primes, length of largest such primes, ...)
* Smallest base such that there is unique prime with period length n.
* Smallest a such that there exists 1<=b<=a such that Phi(n,a,b) is prime.
* Smallest n-digit brilliant number.
* Largest n-digit brilliant number.
* Numbers whose bijective base 26 (with A=1, B=2, ..., Z=26) is a word.
* Primes p such that the absolute value of the fraction A260209(A000720(p)) / (p^3) is a record low (this to Wolstenholme prime is A339855 to Wall-Sun-Sun prime).
* Row n list the possible residue of even perfect number mod n.
* Pell equations: x^2-n*y^2 = +-1, +-2, +-3, +-4. (including: numbers n such that x^2-n*y^2 = -2 is soluble, etc.)
* 15*n+1.
* 32*n+1.
* 31st powers.
* 32nd powers.
* n mod 13.
* The melting point (boiling point) of n-th chamical element in Kelvin (rounded to nearest integer).
* The density of n-th chamical element in kg/m^3 (rounded to nearest integer).
* The year which n-th chamical element was found.
* Conway's game of life (similar to Aliquot sequence) as below (Ulam spiral):

   2^30 2^29 2^28 2^27 2^26 2^25 2^48
   2^31 2^12 2^11 2^10 2^ 9 2^24 2^47
   2^32 2^13 2^ 2 2^ 1 2^ 8 2^23 2^46
   2^33 2^14 2^ 3 2^ 0 2^ 7 2^22 2^45
   2^34 2^15 2^ 4 2^ 5 2^ 6 2^21 2^44
   2^35 2^16 2^17 2^18 2^19 2^20 2^43
   2^36 2^37 2^38 2^39 2^40 2^41 2^42