[seqfan] inches to mm

Jeremy Gardiner jeremy.gardiner at btinternet.com
Sat Jun 12 19:00:16 CEST 2010


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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