A058981 -id:A058981 - cp's OEIS frontend

A058982 Increasing values of the Improperly Reduced Fibonacci Sequence (A058981).

0, 1, 2, 3, 5, 7, 11, 17, 23, 29, 31, 37, 43, 59, 67, 97, 101, 121, 125, 137, 149, 181, 233, 394, 603, 647, 863, 871, 1093, 1665, 2237, 2254, 3113, 4501, 5531, 6137, 8597, 14734, 22511

Offset: 0

Robert G. Wilson v, Jan 15 2001

Cf. A058981.

y = 0; c = l = i = z = 1; d = {1}; Do[ x = y + z; c++; j = 1; While[ ! IntegerQ[ x / d[ [ j ] ] ] && j <= i, j++ ]; If[ j > i, d = Append[ d, x ]; i++, x = x/d[ [ j ] ]; d = Delete[ d, j ]; d = Append[ d, x ] ]; If[ x > l, l = x; Print[ x ] ]; y = z; z = x, {n, 1, 10^7} ]

a(31)-a(38) from Sean A. Irvine, Sep 09 2022

A058983 Position at which increasing values of the Improperly Reduced Fibonacci Sequence (A058981) occur.

Original entry on oeis.org

0, 1, 3, 4, 5, 8, 25, 27, 28, 397, 400, 402, 403, 405, 1398, 1399, 1401, 11300, 11307, 11309, 11310, 11315, 44839, 44840, 44842, 1447644, 6237276, 6237278, 9113438, 9113440, 9113441, 60850032, 176139461, 525738914, 525738917, 2492039442, 2492039443, 2492039444, 2492039446

Offset: 0

Robert G. Wilson v, Jan 15 2001

nonn

Cf. A058981, A058982.

y = 0; c = l = i = z = 1; d = {1}; Do[ x = y + z; c++; j = 1; While[ ! IntegerQ[ x / d[ [ j ] ] ] && j <= i, j++ ]; If[ j > i, d = Append[ d, x ]; i++, x = x/d[ [ j ] ]; d = Delete[ d, j ]; d = Append[ d, x ] ]; If[ x > l, l = x; Print[ c ] ]; y = z; z = x, {n, 1, 10^7} ]

a(31)-a(38) from Sean A. Irvine, Sep 09 2022

A079777 a(0) = 0, a(1) = 1; for n > 1, a(n) = (a(n-1) + a(n-2)) (mod n).

Original entry on oeis.org

0, 1, 1, 2, 3, 0, 3, 3, 6, 0, 6, 6, 0, 6, 6, 12, 2, 14, 16, 11, 7, 18, 3, 21, 0, 21, 21, 15, 8, 23, 1, 24, 25, 16, 7, 23, 30, 16, 8, 24, 32, 15, 5, 20, 25, 0, 25, 25, 2, 27, 29, 5, 34, 39, 19, 3, 22, 25, 47, 13, 0, 13, 13, 26, 39, 0, 39, 39, 10, 49, 59, 37, 24, 61, 11, 72, 7, 2, 9, 11, 20

Offset: 0

Joseph L. Pe, Mar 08 2003

nonn

Robert G. Wilson v, Table of n, a(n) for n = 0..10001 [a(9917) corrected by _Georg Fischer_, Dec 03 2023]

Cf. A000045, A058981, A096534, A096535, Zeros in A073853.

l = {1, 1}; For[i = 3, i <= 100, i++, len = Length[l]; l = Append[l, Mod[l[[len]] + l[[len - 1]], i]]]; l
f[s_] := f[s] = Append[s, Mod[s[[ -2]] + s[[ -1]], Length[s]]]; Nest[f, {0, 1}, 80] (* Robert G. Wilson v, Dec 16 2007 *)
RecurrenceTable[{a[0]==0,a[1]==1,a[n]==Mod[a[n-1]+a[n-2],n]},a,{n,80}] (* Harvey P. Dale, Nov 29 2019 *)

Edited by Robert G. Wilson v, Dec 16 2007

cp's OEIS Frontend

A058982 Increasing values of the Improperly Reduced Fibonacci Sequence (A058981).

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A058983 Position at which increasing values of the Improperly Reduced Fibonacci Sequence (A058981) occur.

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Crossrefs

Programs

Mathematica

Extensions

A079777 a(0) = 0, a(1) = 1; for n > 1, a(n) = (a(n-1) + a(n-2)) (mod n).

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