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Search: id:A111093
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| A111093 |
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Like sequence A111072 but moving right by the squares of the sequence of natural integers. |
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+0
2
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| 0, 1, 6, 10, 10, 15, 16, 16, 20, 25, 30, 36, 36, 45, 50, 50, 56, 61, 70, 70, 70, 71, 76, 80, 80, 85, 86, 86, 90, 95, 100, 106, 106, 115, 120, 120, 126, 131, 140, 140, 140, 141, 146, 150, 150, 155, 156, 156, 160, 165, 170, 176, 176, 185, 190, 190, 196, 201, 210, 210
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Sequences of the form a(n+1) = a(n) + [a(n) - a(n-1) + n^k mod 10] mod 10 with a(0)=0, a(1)=1 and k=1,2,3,4,5, etc. are identical if the exponents "k" differ by 4. Therefore this sequence, where k = 2, is the same as those with exponents 6, 10, 14, 18, etc. - Paolo P. Lava (ppl(AT)spl.at), Sep 29 2006
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FORMULA
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a(n+1) = a(n) + [a(n) - a(n-1) + n^2 mod 10] mod 10 being a(0)=0 and a(1)=1
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EXAMPLE
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Jumping by the squares of the of the sequence of natural integers we move to the numbers 0, 1, 5, 4, 0, 5, 1, 0, 4, 5 etc.
Summing the numbers we obtain 0, 0+1=1, 1+5=6, 6+4=10, 10+0=10, 10+5=15 etc.
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MAPLE
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ANM:=proc(N) global anplus1, anminus1; local an, i; anminus1:=0; an:=1; print (anminus1, an); for i from 2 by 1 to N do anplus1:=an+((an-anminus1+ i^2 mod 10) mod 10); print(anplus1); anminus1:=an; an:=anplus1; od; end: ANM(100);
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CROSSREFS
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Cf. A111072.
Sequence in context: A003862 A127019 A024746 this_sequence A087873 A107014 A132628
Adjacent sequences: A111090 A111091 A111092 this_sequence A111094 A111095 A111096
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KEYWORD
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easy,nonn
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AUTHOR
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Giorgio Balzarotti & Paolo P. Lava (ppl(AT)spl.at), Oct 13 2005
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