[seqfan] Re: inches to mm

[Alonso Del Arte]

This is one of those sequences that doesn't seem terribly interesting but
which we'll be glad to have in the table (as
A169860<http://www.research.att.com/~njas/sequences/A169860>)
a few months down the road when someone submits a sloppy version of it; then
we can just say "It's already in." And it's nice to see that you've put
quite some thought into it.

Al

On Sat, Jun 12, 2010 at 1:00 PM, Jeremy Gardiner <
jeremy.gardiner at btinternet.com> wrote:

>
> Not sure if these sequences are sufficiently interesting for the OEIS:
>
> Culturally significant surely, but maybe mathematically not more
> interesting
> than e.g., A047381 floor(7n/5) or A057355 floor(3n/5)...?
>
> Floor inches to mm
>
> a(n) = floor(n*25.4) = floor(n*127/5)
>
>
> 25,50,76,101,127,152,177,203,228,254,279,304,330,355,381,406,431,457,482,508
>
> ,533,558,584,609,635,660,685,711,736,762,787,812,838,863,889,914,939,965,990
>
> ,1016,1041,1066,1092,1117,1143,1168,1193,1219,1244,1270,1295,1320,1346,1371,
>
> 1397,1422,1447,1473,1498,1524,1549,1574,1600,1625,1651,1676,1701,1727,1752,1
>
> 778,1803,1828,1854,1879,1905,1930,1955,1981,2006,2032,2057,2082,2108,2133,21
>
> 59,2184,2209,2235,2260,2286,2311,2336,2362,2387,2413,2438,2463,2489,2514,254
> 0
>
> Ceiling inches to mm
>
> a(n) = ceiling(n*127/5)
>
>
> 26,51,77,102,127,153,178,204,229,254,280,305,331,356,381,407,432,458,483,508
>
> ,534,559,585,610,635,661,686,712,737,762,788,813,839,864,889,915,940,966,991
>
> ,1016,1042,1067,1093,1118,1143,1169,1194,1220,1245,1270,1296,1321,1347,1372,
>
> 1397,1423,1448,1474,1499,1524,1550,1575,1601,1626,1651,1677,1702,1728,1753,1
>
> 778,1804,1829,1855,1880,1905,1931,1956,1982,2007,2032,2058,2083,2109,2134,21
>
> 59,2185,2210,2236,2261,2286,2312,2337,2363,2388,2413,2439,2464,2490,2515,254
> 0
>
> Cf.
> A029919 Convert n from inches (") to centimeters (cm) a(n)=round(n*254/100)
> A029920 Convert n from centimeters (cm) to inches (")
> A085269 Integer part of the conversion from centimeters to inches
> a(n)=floor(x/2.54)
>
> Parity:
>
>
> 1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,
>
> 0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,
> 1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0
>
> Run lengths in parity:
>
>
> 1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,
> 2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2
>
> This is A130196 Period 3: repeat 1 2 2.
>
> Parity appears to match parity of these sequences:
>
> A034114 Decimal part of square root of a(n) starts with 8: first term of
> runs
> A047332 Numbers that are congruent to {0, 2, 3, 5, 6} mod 7
> A047367 Numbers that are congruent to {0, 1, 3, 4, 5} mod 7
> A047381 Numbers that are congruent to {0, 1, 2, 4, 5} mod 7 a(n)=
> floor(7n/5)
> A057355 Floor(3n/5)
> A065187 "Greedy Dragons" permutation of the natural numbers, inverse of
> A065186
> A160081 Lodumo_5 of Fibonacci numbers
>
> Anti-parity:
>
>
> 0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,
>
> 1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,
> 0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1
>
> Anti-parity appears to match parity of these sequences:
>
> A036404 Ceiling(n^2/5)
> A047299 Numbers that are congruent to {0, 1, 3, 4, 6} mod 7
> A118554 a(n) = 6*a(n-5)-a(n-10)+98 with a(0)=0, a(1)=11, a(2)=35, a(3)=56,
> a(4)=104, a(5)=147, a(6)=204, a(7)=336, a(8)=455, a(9)=731
> A032796 Numbers that are congruent to {1, 2, 3, 5, 6} mod 7
> A028841 Iterated sum of digits of n is a Fibonacci number
> A047317 Numbers that are congruent to {1, 2, 4, 5, 6} mod 7
> A034108 Decimal part of square root of a(n) starts with 2: first term of
> runs
>
> ---------------
> Jeremy Gardiner
>
>
>
>
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