Number of the day: 2971

Properties of the number 2971:

2971 is a cyclic number.
2969 and 2971 form a twin prime pair.
2971 has 9 antidivisors and 2970 totatives.
2971 has a prime digit sum 19 in base 10.
2971 = (43 × 44)/2 + … + (45 × 46)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
2971 = 1486² - 1485² is the difference of 2 nonnegative squares in 1 way.
2971 is the sum of 2 positive triangular numbers.
2971 is the difference of 2 positive pentagonal numbers in 1 way.
2971 = 19² + 33² + 39² is the sum of 3 positive squares.
2971² is the sum of 3 positive squares.
2971 is a proper divisor of 1627¹¹ - 1.
2971 = '2' + '971' is the concatenation of 2 prime numbers.
2971 is an emirp in (at least) the following bases: 7, 11, 15, 20, 27, 41, 44, 50, 51, 55, 59, 61, 62, 63, 72, 76, and 100.
2971 is palindromic in (at least) the following bases: 16, 28, 45, 54, -55, -66, -90, and -99.
2971 in base 16 = b9b and consists of only the digits '9' and 'b'.
2971 in base 28 = 3m3 and consists of only the digits '3' and 'm'.
2971 in base 38 = 227 and consists of only the digits '2' and '7'.
2971 in base 44 = 1NN and consists of only the digits '1' and 'N'.
2971 in base 45 = 1L1 and consists of only the digits '1' and 'L'.
2971 in base 53 = 133 and consists of only the digits '1' and '3'.
2971 in base 54 = 111 and consists of only the digit '1'.

The number 2971 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000230: Smallest prime p such that there is a gap of 2n between p and next prime.
A001605: Indices of prime Fibonacci numbers.
A002383: Primes of form n^2 + n + 1.
A005448: Centered triangular numbers: a(n) = 3n(n-1)/2 + 1.
A040016: Largest prime < e^n.
A054569: a(n) = 4*n^2 - 6*n + 3.
A061323: Primes with 10 as smallest positive primitive root.
A081256: Greatest prime factor of n^3 + 1.
A085104: Primes of the form 1 + n + n^2 + n^3 + ... + n^k, n > 1, k > 1.
A124993: Primes of the form 22k+1 generated recursively. Initial prime is 23. General term is a(n)=Min {p is prime; p divides (R^11 - 1)/(R - 1); Mod[p,11]=1}, where Q is the product of previous terms in the sequence and R = 11Q.