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Search: id:A128252
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| A128252 |
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T(n,m) is the smallest number that starts a sequence of n+1 consecutive integers whose Euler totient Functions are multiples of m. |
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+0
1
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| 0, 0, 3, 0, 3, 13, 0, 3, 26, 12, 0, 3, 35, 15, 61, 0, 3, 35, 32, 99, 13, 0, 3, 151, 32, 121, 26, 86, 0, 3, 151, 32, 121, 35, 637, 15, 0, 3, 151, 72, 3688, 35, 841, 15, 37, 0, 3, 727, 108, 5608, 151, 2694, 87, 216, 61, 0, 3, 1453, 108, 5697, 151, 66668, 87, 216, 99, 267
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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T(n,m) is the smallest 'a' such that all A000010(a+i), 0<=i<=n, are multiples of m. T(7,3)=151 because phi(151)=2*3*5, phi(152)=2^3*3^2, phi(153)=2^5*3 up to phi(158)=2*3*13 are all multiples of 3, and the numbers up to 150 do not start such a run of 8 elements. Table is read along antidiagonals.
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REFERENCES
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Ho-Joo Lee, Consecutive Integers whose totients are multiples of n, Solution to
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EXAMPLE
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n\m.1.2....3...4.....5....6.......7...8.....9....10
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1|..0.3...13..12....61...13......86..15....37....61.
2|..0.3...26..15....99...26.....637..15...216....99.
3|..0.3...35..32...121...35.....841..87...216...121.
4|..0.3...35..32...121...35....2694..87..1082...121.
5|..0.3..151..32..3688..151...66668.230..2916..3688.
6|..0.3..151..72..5608..151..168252.285..2916..5608.
7|..0.3..151.108..5697..151..168252.285..2916..5697.
8|..0.3..727.108.31800..727.1201204.403.37366.31800.
9|..0.3.1453.108.31800.1453.1201204.798.48505.31800
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MAPLE
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T := proc(n, m) local a, i, fail ; a :=0 ; while true do fail := false ; for i from 0 to n do if numtheory[phi](a+i) mod m <> 0 then fail := true ; break ; fi ; od ; if fail = false then RETURN(a) ; else a := a+1 ; fi ; od ; end: for d from 2 to 12 do for n from d-1 to 1 by -1 do printf("%d, ", T(n, d-n)) ; od ; od;
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CROSSREFS
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Sequence in context: A021333 A104141 A060533 this_sequence A033596 A063529 A136667
Adjacent sequences: A128249 A128250 A128251 this_sequence A128253 A128254 A128255
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KEYWORD
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nonn,tabl
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 03 2007
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