A073259 -id:A073259 - cp's OEIS frontend

A073320 A073259(n)=3: the length of iteration transient leading to n-th composite number equals 3.

4, 5, 8, 9, 13, 16, 17, 18, 22, 23, 24, 27, 31, 35, 36, 40, 41, 46, 47, 56, 64, 69, 70, 71, 89, 90, 91, 92, 93, 94, 95, 103, 109, 110, 111, 112, 113, 146, 147, 161, 162, 163, 171, 172, 173, 174, 196, 240, 241, 242, 243, 261, 262, 263, 277, 438, 439, 440, 1137, 1138

Offset: 1

Labos Elemer, Jul 29 2002

			The sequence is most probably complete. a(1)=4: the fixed point list from m=a(1) to composite[m] is: {4,7,9}, the length is 3; last term is a(64)=1142 with transient list {1142,1332,1360}.

Cf. A002808, A073259.

lfp[x_] := Length[FixedPointList[x+PrimePi[ # ]+1&, x]]-1 Do[s=lfp[n]; If[Equal[s, 3], Print[n]], {n, 1, 10000000}]

See Program.

A073322 a(n)=A073259[A002808(n)] and a(0)=3; Length of FixedPointList started with n-th nonprime and leading to corresponding composite number= c[c(n)].

Original entry on oeis.org

3, 4, 3, 3, 4, 4, 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 4, 4, 4, 4, 4, 3, 3, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 5, 4, 4, 3, 4, 4, 5, 4, 4, 3, 4, 4, 4, 3, 3, 4, 4, 4, 5, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 5, 4, 4, 4, 5, 4, 4, 3, 3, 3, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4

Offset: 0

Labos Elemer, Jul 29 2002

nonn

			list to n=0 corresponding to c[0]=1: {1,2,3,4} started with first nonprime ended with first composite; n=10: composite[10]=18, a(10)=length[{16,26,28}]=3.

Cf. A002808, A073259, A073260.

c[x_] := FixedPoint[x+c[ # ]+1&, x] lfp[x_] := Length[FixedPointList[x+c[ # ]+1&, x]]-1 Table[lfp[c[w]]-1, {w, 1, 128}]

See Program.

A073321 a(n)=A073259[A000040(n)]; Length of FixedPointList started with n-th prime and leading to corresponding composite number.

Original entry on oeis.org

4, 4, 3, 4, 4, 3, 3, 4, 3, 5, 3, 4, 3, 5, 3, 4, 4, 4, 4, 3, 4, 5, 5, 3, 4, 4, 3, 4, 3, 3, 4, 4, 4, 5, 5, 4, 4, 3, 4, 3, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 3, 5, 4, 3, 5, 4, 3, 4, 5, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 6, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 5, 4, 4, 6, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4

Offset: 1

Labos Elemer, Jul 29 2002

nonn

			a=10,p(10)=29, list={29,40,42,43,44}.

Cf. A002808, A073259.

lfp[x_] := Length[FixedPointList[x+PrimePi[ # ]+1&, x]]-1 Table[lfp[Prime[w]]-1, {w, 1, 128}]

See Program.

A073323 Smallest k such that A073259(k)=n or 0 if there is no such value; the first number of which length of fixed-point-list terminated by k-th composite number equals n.

Original entry on oeis.org

0, 0, 4, 1, 29, 153, 4913, 73114, 1985627, 69912446, 2734947158

Offset: 1

Labos Elemer, Jul 29 2002

Occurrences of lengths [1-10] for n<=10000000 are {0,0,64,4662,310495,6468633,3041909,173579,658,0}.

			For lengths n=3, 4, 5, 6, 7, 8 the corresponding lists are: {4, 7, 9}, {1, 2, 3, 4}, {29, 40, 42, 43, 44}, {153, 190, 196, 198, 199, 200}, {4913, 5570, 5649, 5656, 5658, 5659, 5660} and {73114, 80343, 80982, 81039, 81046, 81048, 81049, 81050}.

Cf. A002808, A073259, A073320-A073322.

lfp[x_] := Length[FixedPointList[x + PrimePi[ # ] + 1 &, x]]-1 t=Table[0, {15}]; Do[s=lfp[n]; If[s<16&&t[[s]]==0, t[[s]]=n], {n, 1, 100000}]; t

a(n) = Min{k: A073259(k)=n}

a(10)-a(11) from Sean A. Irvine, Nov 22 2024

A073439 Numbers k such that A073259(k)=4: the length of iteration-transient leading to k-th composite number equals 4.

Original entry on oeis.org

1, 2, 3, 6, 7, 10, 11, 12, 14, 15, 19, 20, 21, 25, 26, 28, 30, 32, 33, 34, 37, 38, 39, 42, 44, 45, 48, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 72, 73, 74, 75, 77, 78, 81, 82, 84, 85, 86, 87, 88, 96, 97, 98, 100, 101, 102, 104, 106, 107, 108, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 129, 130, 131, 132, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 148

Offset: 1

Labos Elemer, Jul 31 2002

nonn

			The sequence is probably finite and given in full. a(1)=1: the fixed point list from m=a(1) to composite[m] is: {1,2,3,4}, the length is 4; largest term seems to be a(4662)=77629, with transient list {77629,85259,85933,85990}. The terms appears in bursts of consecutive integers. A chain of 37 consecutive numbers starts at 28046.

Sean A. Irvine, Table of n, a(n) for n = 1..4662

Cf. A002808, A073259, A073320.

lfp[x_] := Length[FixedPointList[x+PrimePi[ # ]+1&, x]]-1 Do[s=lfp[n]; If[Equal[s, 4], Print[n]], {n, 1, 10000000}]

Offset corrected by Sean A. Irvine, Nov 28 2024

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A073320 A073259(n)=3: the length of iteration transient leading to n-th composite number equals 3.

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A073322 a(n)=A073259[A002808(n)] and a(0)=3; Length of FixedPointList started with n-th nonprime and leading to corresponding composite number= c[c(n)].

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A073321 a(n)=A073259[A000040(n)]; Length of FixedPointList started with n-th prime and leading to corresponding composite number.

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A073323 Smallest k such that A073259(k)=n or 0 if there is no such value; the first number of which length of fixed-point-list terminated by k-th composite number equals n.

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A073439 Numbers k such that A073259(k)=4: the length of iteration-transient leading to k-th composite number equals 4.

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