## Saturday, 23 March 2013

### SATURDAY, 23 MARCH 2013

Today is the $82^{nd}$ day of the year.

$82 = 2 \times 41$. Since $2$ and $41$ are both prime then $82$ is a semi-prime, see A001358.

$82 = 3^2 + 3^2 + 8^2$

The following calculations all result in prime numbers and all, amazingly, represent sequences that are in OEIS:
A097480: $(2 \times 82) - 15 = 149$
A097363: $(2 \times 82) - 13 = 151$
A089192: $(2 \times 82) - 7 = 157$
A006254: $(2 \times 82) - 1 = 163$
A067076: $(2 \times 82) + 3 = 167$
A155722: $(2 \times 82) + 9 = 173$
A089559: $(2 \times 82) + 15 = 179$
A173059: $(2 \times 82) + 17 = 181$
A095278: $(4 \times 82) + 3 = 331$
A033868: $(7 \times 82) - 11 = 563$
A105133: $(8 \times 82) + 5 = 661$
A007811: $(10 \times 82) + 1 = 821$
A007811: $(10 \times 82) + 3 = 823$
A007811: $(10 \times 82) + 7 = 827$
A007811: $(10 \times 82) + 9 = 829$
A127575: $(16 \times 82) + 15 = 1,327$
A201816: $(90 \times 82) + 13 = 7,393$
A198382: $(90 \times 82) + 37 = 7,417$
A027861: $82^2 + (82 + 1)^2 = 13,613$
A090563: $(5 \times 82^2) + (5 \times 82) + 1 = 34,031$
A125881: $82^3 + 82^2 - 1 = 558,091$
A000068: $82^4 + 1 = 45,212,177$
A139065: $\frac {7 + 82!}{7}$
A139063: $\frac {6 + 82!}{6}$
A007749: $82!! - 1$

I cannot calculate the last three. In fact I doubt anyone can calculate the last one because it would just take too long to calculate the factorial of
$475,364,333,701,284,174,842,138,206,989,404,946,643,813,294,067,993,328,617,160,934,076,743,994,734,899,148,613,007,131,808,479,167,119,360,000,000,000,000,000,000$