Thursday, April 26, 2018

Number of the day: 73037

Properties of the number 73037:

73037 is a cyclic number.
73037 and 73039 form a twin prime pair.
73037 has 19 antidivisors and 73036 totatives.
73037 has an oblong digit sum 20 in base 10.
73037 = 193 + 193 + 393 is the sum of 3 positive cubes in 1 way.
73037 = 365192 - 365182 is the difference of 2 nonnegative squares in 1 way.
73037 is the difference of 2 positive pentagonal numbers in 1 way.
73037 = 262 + 2692 is the sum of 2 positive squares in 1 way.
73037 = 42 + 112 + 2702 is the sum of 3 positive squares.
730372 = 139882 + 716852 is the sum of 2 positive squares in 1 way.
730372 is the sum of 3 positive squares.
73037 is a proper divisor of 647589 - 1.
73037 = '7' + '3037' is the concatenation of 2 prime numbers.
73037 is an emirp in (at least) the following bases: 4, 5, 9, 11, 13, 14, 20, 23, 28, 34, 36, 39, 40, 44, 47, 49, 54, 56, 57, 58, 61, 62, 71, 73, 74, 80, 89, 93, 96, 99, and 100.
73037 is a palindrome (in base 10).
73037 is palindromic in (at least) the following bases: 42, -46, and -61.
73037 in base 42 = fGf and consists of only the digits 'G' and 'f'.
73037 in base 60 = KHH and consists of only the digits 'H' and 'K'.

The number 73037 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A052024: Every suffix of palindromic prime a(n) is prime (left-truncatable).
A062352: Palindromic primes with strictly decreasing digits up to the middle and then strictly increasing.
A081220: Palindromic primes = 1 mod 4.
A082769: a(n) = smallest palindromic prime that begins with A082768(n), or 0 if no such number exists.
A083840: Palindromic primes which are a member of a twin prime pair.
A083841: Palindromic primes p such that p+2 is also a prime: members of A083840 which are the smaller member of a twin prime pair.
A088269: Palindromic primes that yield a prime when sandwiched between two 1's. (Prefixing and suffixing a one on both sides yields another pal prime).
A109184: Palindromic primes with digit sum 20.
A136098: Prime palindromic cyclops numbers.
A260378: Primes that contain only the digits (0, 3, 7).

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