[seqfan] Similar sequences A059270, A163396 and A133767 (mod 27)

Jeremy Gardiner jeremy.gardiner at btinternet.com
Thu Aug 19 12:00:06 CEST 2010


While scanning the alphabetised version of the database, I noticed the
following similarities:

A059270      cooiccorruffuufiilxxrllxcooiccorruff
A163396      cooiccorruffuufiilxxrllxcooiccorruff
A133767 xrllxcooiccorruffuufiilxxrll

A059270 Numbers which are both the sum of n+1 consecutive integers and the
sum of the n immediately higher consecutive integers.

0, 3, 15, 42, 90, 165, 273, 420, 612, 855, 1155, 1518, 1950, 2457, 3045,
3720, 4488, 5355, 6327, 7410, 8610, 9933, 11385, 12972, 14700, 16575, 18603,
20790, 23142, 25665, 28365, 31248, 34320, 37587, 41055, 44730, 48618, 52725,
57057, 61620

A163396 a(n)=(product_{x=n-th even number..n-th even nonprime}x)/8

0, 3, 15, 42, 90, 165, 273, 420, 612, 855, 1155, 1518, 1950, 2457, 3045,
3720, 4488, 5355, 6327, 7410, 8610, 9933, 11385, 12972, 14700, 16575, 18603,
20790, 23142, 25665, 28365, 31248, 34320, 37587, 41055, 44730, 48618, 52725,
57057, 61620

a(n) mod 27 = 
3,15,15,9,3,3,15,18,18,21,6,6,21,21,6,9,9,12,24,24,18,12,12,24,3,15,15,9,3,3
,15,18,18,21,6,6

A133767         a(n) = (4*n+3)*(4*n+5)*(4*n+7).

105, 693, 2145, 4845, 9177, 15525, 24273, 35805, 50505, 68757, 90945,
117453, 148665, 184965, 226737, 274365, 328233, 388725, 456225, 531117,
613785, 704613, 803985, 912285, 1029897, 1157205, 1294593, 1442445, 1601145,
1771077, 1952625

a(n) mod 27 = 
24,18,12,12,24,3,15,15,9,3,3,15,18,18,21,6,6,21,21,6,9,9,12,24,24,18,12,12






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