John Cerkan - cp's OEIS frontend

A278932 Numbers n such that n remains prime through 6 iterations of function f(x) = 2x + 1.

1122659, 2164229, 2329469, 10257809, 10309889, 12314699, 14030309, 14145539, 19099919, 23103659, 24176129, 28843649, 37088729, 38199839, 42389519, 49160099, 50785439, 52554569, 62800169, 68718059, 85864769, 88174049, 95831189, 105109139, 105388169

Offset: 1

John Cerkan, Dec 01 2016

nonn

n, 2*n+1, 4*n+3, 8*n+7, 16*n+15, 32*n+31, and 64*n+63 are primes.

a(n) == 29 (mod 30).

Subsequence of A007700, A023272, A023302, and A023330.

a005408(n) = 2*n+1
count(n) = my(k=n, i=0); while(ispseudoprime(k), k=a005408(k); i++); i
is(n) = count(n) > 6 \\ Felix Fröhlich, Dec 05 2016

A273971 Numbers y such that there exists a pair x, n, with x < y, x != n and y != n that makes {x,y,n,n} an amicable multiset.

Original entry on oeis.org

756000, 803040, 1267560, 1442448, 1851360, 2535120, 3209760, 3477240, 3926160, 3969840, 4413240, 4664880, 6094368, 6840540, 7617960, 7783020, 8027880, 8360352, 8586900, 9215640, 9559200, 9596520, 9697380, 9811620, 9815400, 9938160, 10063200, 10234224

Offset: 1

John Cerkan, Jul 17 2016

nonn

We call the multiset {x,y,n,n} amicable iff sigma(x) = sigma(y) = sigma(n) = x+y+n+n. For the n values, see A273969. For the x values, see A273970.

If the condition xA259306 would also belong here.

			sigma(695520) = sigma(803040) = sigma(702240) = 695520 + 803040 + 702240 + 702240.

John Cerkan, Table of n, a(n) for n = 1..7515
John Cerkan, Python code

Cf. A259302, A259303, A259304, A259305, A259306, A273969, A273970.

A273970 Numbers x such that there exist a pair y, n with x < y, x != n and y != n that makes {x,y,n,n} an amicable multiset.

Original entry on oeis.org

695520, 753480, 1113840, 1136520, 1784160, 2313360, 2898720, 3140280, 3865680, 3960600, 4272840, 4500720, 4626720, 6126120, 6167700, 7197960, 7442820, 7731360, 8177400, 8498700, 8784720, 8828820, 8920800, 8966160, 9124920, 9232860, 9664200, 9729720

Offset: 1

John Cerkan, Jul 17 2016

nonn

We call the multiset {x,y,n,n} amicable iff sigma(x) = sigma(y) = sigma(n) = x+y+n+n. For the n values, see A273969. For the y values, see A273971.

If the condition xA259306 would also belong here.

			sigma(695520) = sigma(803040) = sigma(702240) = 695520 + 803040 + 702240 + 702240.

John Cerkan, Table of n, a(n) for n = 1..8060
John Cerkan, Python code

Cf. A259302, A259303, A259304, A259305, A259306, A273969, A273971.

A273969 Numbers n such that there exists a pair x,y, where x

Original entry on oeis.org

702240, 817740, 1156680, 1159200, 1811040, 2450448, 2570400, 2784600, 3534300, 3912480, 4228560, 4546080, 4702320, 5682600, 6902280, 7280280, 7469280, 7706160, 8225280, 8316000, 8465184, 8522640, 8639400, 9025380, 9256800, 9282000, 9492120, 9828000

Offset: 1

John Cerkan, Jul 17 2016

nonn

We call the multiset {x,y,n,n} amicable iff sigma(x) = sigma(y) = sigma(n) = x+y+n+n. For the x values, see A273970. For the y values, see A273971.

If the condition xA259306 would also belong here.

			sigma(695520) = sigma(803040) = sigma(702240) = 695520 + 803040 + 702240 + 702240.

John Cerkan, Table of n, a(n) for n = 1..8082
John Cerkan, Python code

Cf. A259302, A259303, A259304, A259305, A259306, A273970, A273971.

A273936 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Original entry on oeis.org

294821130240, 350100092160, 368526412800, 457350727680, 457350727680, 466800122880, 466800122880, 466800122880, 522686545920

Offset: 1

John Cerkan, Jun 04 2016

The 5-tuple starting with 53542288800 was given by Donovan Johnson. The common value of sigma(x) is 294821130240.
A larger 5-tuple, (55766707476480, 56992185169920, 57515254917120, 57754372515840, 57829096765440), was found by Michel Marcus on Dec 09 2013. The common value of sigma(x) is 285857616844800.
A still larger example (227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800), probably the first one to be published, had been found by Yasutoshi Kohmoto in 2008, cf. link to SeqFan post.
Other terms from John Cerkan.
There are different definitions for amicable k-tuples, cf. link to MathWorld.

John Cerkan, More terms, with gaps.
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Nov 23 2008
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Dec 09 2013
Eric W. Weisstein, Amicable Triple. From MathWorld--A Wolfram Web Resource.

Cf. A233553, A273928, A273930, A273931, A273933, A273934 (5-tuples).
Cf. A036471 - A036474 and A116148 (quadruples).
Cf. A125490 - A125492 and A137231 (triples).

A273934 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Original entry on oeis.org

61695597600, 72598125600, 78953074200, 96369633360, 96369633360, 103073639760, 99692021520, 100469023200, 109446377040

Offset: 1

John Cerkan, Jun 04 2016

The 5-tuple starting with 53542288800 was given by Donovan Johnson. The common value of sigma(x) is 294821130240.
A larger 5-tuple, (55766707476480, 56992185169920, 57515254917120, 57754372515840, 57829096765440), was found by Michel Marcus on Dec 09 2013. The common value of sigma(x) is 285857616844800.
A still larger example (227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800), probably the first one to be published, had been found by Yasutoshi Kohmoto in 2008, cf. link to SeqFan post.
Other terms from John Cerkan.
There are different definitions for amicable k-tuples, cf. link to MathWorld.

John Cerkan, More terms, with gaps.
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Nov 23 2008
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Dec 09 2013
Eric W. Weisstein, Amicable Triple. From MathWorld--A Wolfram Web Resource.

Cf. A233553, A273928, A273930, A273931, A273933, A273936 (5-tuples).
Cf. A036471 - A036474 and A116148 (quadruples).
Cf. A125490 - A125492 and A137231 (triples).

A273933 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Original entry on oeis.org

60074174160, 71957405520, 75710489400, 96058282320, 96058282320, 97306569360, 96759542880, 94972878000, 109117562400

Offset: 1

John Cerkan, Jun 04 2016

The 5-tuple starting with 53542288800 was given by Donovan Johnson. The common value of sigma(x) is 294821130240.
A larger 5-tuple, (55766707476480, 56992185169920, 57515254917120, 57754372515840, 57829096765440), was found by Michel Marcus on Dec 09 2013. The common value of sigma(x) is 285857616844800.
A still larger example (227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800), probably the first one to be published, had been found by Yasutoshi Kohmoto in 2008, cf. link to SeqFan post.
Other terms from John Cerkan.
There are different definitions for amicable k-tuples, cf. link to MathWorld.

John Cerkan, More terms, with gaps.
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Nov 23 2008
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Dec 09 2013
Eric W. Weisstein, Amicable Triple. From MathWorld--A Wolfram Web Resource.

Cf. A233553, A273928, A273930, A273931, A273934, A273936 (5-tuples).
Cf. A036471 - A036474 and A116148 (quadruples).
Cf. A125490 - A125492 and A137231 (triples).

A273931 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Original entry on oeis.org

59999219280, 69626138400, 73605331800, 89398663200, 89398663200, 90391981680, 94320626400, 94832992800, 103169959200

Offset: 1

John Cerkan, Jun 04 2016

The 5-tuple starting with 53542288800 was given by Donovan Johnson. The common value of sigma(x) is 294821130240.
A larger 5-tuple, (55766707476480, 56992185169920, 57515254917120, 57754372515840, 57829096765440), was found by Michel Marcus on Dec 09 2013. The common value of sigma(x) is 285857616844800.
A still larger example (227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800), probably the first one to be published, had been found by Yasutoshi Kohmoto in 2008, cf. link to SeqFan post.
Other terms from John Cerkan.
There are different definitions for amicable k-tuples, cf. link to MathWorld.

John Cerkan, More terms, with gaps.
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Nov 23 2008
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Dec 09 2013
Eric Weisstein's World of Mathematics, Amicable Triple.

Cf. A233553, A273928, A273930, A273933, A273934, A273936 (5-tuples).
Cf. A036471 - A036474 and A116148 (quadruples).
Cf. A125490 - A125492 and A137231 (triples).

A273930 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Original entry on oeis.org

59509850400, 68763895200, 72747675000, 88410722400, 88021533600, 89894684880, 89894684880, 90391981680, 102481394400

Offset: 1

John Cerkan, Jun 04 2016

The 5-tuple starting with 53542288800 was given by Donovan Johnson. The common value of sigma(x) is 294821130240.
A larger 5-tuple, (55766707476480, 56992185169920, 57515254917120, 57754372515840, 57829096765440), was found by Michel Marcus on Dec 09 2013. The common value of sigma(x) is 285857616844800.
A still larger example (227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800), probably the first one to be published, had been found by Yasutoshi Kohmoto in 2008, cf. link to SeqFan post.
Other terms from John Cerkan.
There are different definitions for amicable k-tuples, cf. link to MathWorld.

John Cerkan, More terms, with gaps.
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Nov 23 2008
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Dec 09 2013
Eric W. Weisstein, Amicable Triple. From MathWorld--A Wolfram Web Resource.

Cf. A233553, A273928, A273931, A273933, A273934, A273936 (5-tuples).
Cf. A036471 - A036474 and A116148 (quadruples).
Cf. A125490 - A125492 and A137231 (triples).

A273928 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Original entry on oeis.org

53542288800, 67154527440, 67509842400, 87113426400, 87502615200, 86133247200, 86133247200, 86133247200, 98471252880

Offset: 1

John Cerkan, Jun 04 2016

The 5-tuple starting with 53542288800 was given by Donovan Johnson. The common value of sigma(x) is 294821130240.
A larger 5-tuple, (55766707476480, 56992185169920, 57515254917120, 57754372515840, 57829096765440), was found by Michel Marcus on Dec 09 2013. The common value of sigma(x) is 285857616844800.
A still larger example (227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800), probably the first one to be published, had been found by Yasutoshi Kohmoto in 2008, cf. link to SeqFan post.
Other terms from John Cerkan.
There are different definitions for amicable k-tuples, cf. link to MathWorld.

John Cerkan, More terms with gaps.
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Nov 23 2008
Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Dec 09 2013
Eric W. Weisstein, Amicable Triple. From MathWorld--A Wolfram Web Resource.

Cf. A233553, A273930, A273931, A273933, A273934, A273936 (5-tuples).
Cf. A036471 - A036474 and A116148 (quadruples).
Cf. A125490 - A125492 and A137231 (triples).

cp's OEIS Frontend

User: John Cerkan

A278932 Numbers n such that n remains prime through 6 iterations of function f(x) = 2x + 1.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A273971 Numbers y such that there exists a pair x, n, with x < y, x != n and y != n that makes {x,y,n,n} an amicable multiset.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A273970 Numbers x such that there exist a pair y, n with x < y, x != n and y != n that makes {x,y,n,n} an amicable multiset.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A273969 Numbers n such that there exists a pair x,y, where x

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A273936 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Views

Author

Keywords

Comments

Links

Crossrefs

A273934 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Views

Author

Keywords

Comments

Links

Crossrefs

A273933 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Views

Author

Keywords

Comments

Links

Crossrefs

A273931 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Views

Author

Keywords

Comments

Links

Crossrefs

A273930 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Views

Author

Keywords

Comments

Links

Crossrefs

A273928 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5, x1

Views

Author

Keywords

Comments

Links

Crossrefs