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A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation.. For example, there is a near-equality close to the round number 1000 between powers of 2 and powers of 10:
Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
Every prime number p divides a Fibonacci number that can be determined by the value of p modulo 5. If p is congruent to 1 or 4 modulo 5, then p divides F p−1, and if p is congruent to 2 or 3 modulo 5, then, p divides F p+1. The remaining case is that p = 5, and in this case p divides F p.
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1: 3: 5: 7: 9: 11: 13: 15: 17: 19: 21: 23: 25 The first number remaining in the list after 1 is 3, so every third number (beginning at 1) which remains in the list (not every multiple of 3) is eliminated. The first of these is 5: 1: 3: 7: 9: 13: 15: 19: 21: 25 The next surviving number is now 7, so every seventh remaining number is eliminated ...
There are 92 elements containing the digits 1, 2, and 3 only, which John Conway named after the 92 naturally-occurring chemical elements up to uranium, calling the sequence audioactive. There are also two "transuranic" elements (Np and Pu) for each digit other than 1, 2, and 3. [5] [6] Below is a table of all such elements:
Rates on a 15-year mortgage stand at an average 5.94% for purchase and 5.95% for refinance — down 21 basis points from 6.15% for purchase and 25 basis points from 6.20% for refinance this time ...
10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10; n natural: 10 19 109 199 1099 1999 10999 19999 109999 199999 n even: 5 9 49 89 489 889 4889 8889 48889 88889 n odd ...