Thursday, October 8, 2020

Number of the day: 9781

Properties of the number 9781:

9781 is a cyclic number.
9781 is the 1206th prime.
9781 has 5 antidivisors and 9780 totatives.
9781 has a semiprime digit sum 25 in base 10.
9781 has sum of divisors equal to 9782 which is a sphenic number.
Reversing the decimal digits of 9781 results in an emirp.
9781 = 23 + 83 + 213 is the sum of 3 positive cubes in 1 way.
9781 = 48912 - 48902 is the difference of 2 nonnegative squares in 1 way.
9781 is the sum of 2 positive triangular numbers.
9781 is the difference of 2 positive pentagonal numbers in 1 way.
9781 = 412 + 902 is the sum of 2 positive squares in 1 way.
9781 = 362 + 492 + 782 is the sum of 3 positive squares.
97812 = 64192 + 73802 is the sum of 2 positive squares in 1 way.
97812 is the sum of 3 positive squares.
9781 is a proper divisor of 35910 - 1.
9781 = '9' + '781' is the concatenation of 2 semiprime numbers.
9781 is an emirp in (at least) the following bases: 6, 9, 10, 15, 17, 18, 19, 20, 21, 27, 31, 36, 37, 43, 44, 52, 55, 56, 59, 69, 70, 71, 75, 76, 78, 83, 84, 86, 87, 89, 93, 94, 95, and 99.
9781 is palindromic in (at least) the following bases: -47, and -77.

The number 9781 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A074341: a(1) = 4; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A085013: a(1) = 1; for n>1, a(n) = smallest prime > a(n-1) such that a(1)*...*a(n) + 2 is a prime.
A089442: Primes p such that (p-11)/10 is also a prime.
A139489: Primes of the form x^2+101y^2.
A142122: Primes congruent to 13 mod 37.
A199936: Total sum of Fibonacci parts in all partitions of n.
A206610: Fibonacci sequence beginning 13, 8.
A262508: Numbers that occur only once in A155043; positions of zeros in A262505, ones in A262507.
A299110: Prime(r) for r such that prime(r) - prime(r-1) = 12 and prime(r-1) - prime(r-2) = 2.
A300334: Primes of a056240-type 2.

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