cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A152865 Beginnings of maximal chains of primes with two members (one link).

Original entry on oeis.org

29, 37, 109, 131, 251, 269, 293, 359, 389, 401, 449, 461, 491, 547, 569, 607, 631, 743, 757, 857, 887, 971, 1109, 1151, 1163, 1187, 1289, 1301, 1319, 1373, 1427, 1453, 1499, 1613, 1667, 1801, 1831, 1879, 1913, 1979, 2003, 2029, 2137, 2243, 2377, 2393, 2459
Offset: 1

Views

Author

Klaus Brockhaus, Dec 17 2008

Keywords

Comments

For definitions see A152658, of which this is a subsequence.

Examples

			Second maximal chain of primes with two members (one link) is 37, 41; the linking prime is 977.

Links

Crossrefs

Cf. A152658 (beginnings of maximal chains of primes), A152735 (count of links in n-th maximal chain of primes), A152962 (beginning of the first maximal chain of primes with n links), A152866, A152867, A152868, A152869, A152963, A152964.

Programs

  • PARI
    {n=1; while(n<365, c=0; a=prime(n); while(isprime(n*prime(n)+(n+1)*prime(n+1)), c++; n++); if(c==1, print1(a, ",")); n++)}

A152866 Beginnings of maximal chains of primes with three members (two links).

Original entry on oeis.org

5, 43, 139, 227, 277, 773, 947, 991, 1237, 1481, 1549, 1601, 1871, 1993, 2339, 3119, 3169, 3217, 3259, 3371, 3709, 3853, 4013, 4219, 4483, 4951, 5051, 5107, 5147, 5419, 5527, 6637, 6977, 7477, 7699, 8539, 10139, 10267, 11783, 11981, 12163, 12263
Offset: 1

Views

Author

Klaus Brockhaus, Dec 17 2008

Keywords

Comments

For definitions see A152658, of which this is a subsequence.

Examples

			First maximal chain of primes with three members (two links) is 5, 7, 11; the linking primes are 43, 83.

Links

Crossrefs

Cf. A152658 (beginnings of maximal chains of primes), A152735 (count of links in n-th maximal chain of primes), A152962 (beginning of the first maximal chain of primes with n links), A152865, A152867, A152868, A152869, A152963, A152964.

Programs

  • PARI
    {n=1; while(n<1470, c=0; a=prime(n); while(isprime(n*prime(n)+(n+1)*prime(n+1)), c++; n++); if(c==2, print1(a, ",")); n++)}

A152867 Beginnings of maximal chains of primes with four members (three links).

Original entry on oeis.org

13, 89, 809, 4561, 6689, 7603, 11321, 16493, 18229, 22153, 24107, 28409, 28687, 29153, 32749, 33013, 54493, 55663, 63337, 63419, 67169, 86011, 90289, 108881, 113647, 116929, 132589, 133187, 136033, 136403, 137791, 145543, 147353, 150583
Offset: 1

Views

Author

Klaus Brockhaus, Dec 17 2008

Keywords

Comments

For definitions see A152658, of which this is a subsequence.

Examples

			First maximal chain of primes with four members (three links) is 13, 17, 19, 23; the linking primes are 197, 271, 359.

Links

Crossrefs

Cf. A152658 (beginnings of maximal chains of primes), A152735 (count of links in n-th maximal chain of primes), A152962 (beginning of the first maximal chain of primes with n links), A152865, A152866, A152868, A152869, A152963, A152964.

Programs

  • PARI
    {n=1; while(n<13900, c=0; a=prime(n); while(isprime(n*prime(n)+(n+1)*prime(n+1)), c++; n++); if(c==3, print1(a, ",")); n++)}

A152868 Beginnings of maximal chains of primes with five members (four links).

Original entry on oeis.org

61, 1069, 2293, 2879, 5441, 20347, 145823, 183949, 187171, 207629, 219649, 278087, 412171, 420467, 421273, 507503, 536479, 696937, 698311, 774929, 792283, 1028081, 1310137, 1432927, 1470757, 1726211, 1803881, 1861817, 1904477, 1928561
Offset: 1

Views

Author

Klaus Brockhaus, Dec 17 2008

Keywords

Comments

For definitions see A152658, of which this is a subsequence.

Examples

			First maximal chain of primes with five members (four links) is 61, 67, 71, 73, 79; the linking primes are 2371, 2693, 2953, 3271.

Links

Crossrefs

Cf. A152658 (beginnings of maximal chains of primes), A152735 (count of links in n-th maximal chain of primes), A152962 (beginning of the first maximal chain of primes with n links), A152865, A152866, A152867, A152869, A152963, A152964.

Programs

  • PARI
    {n=1; while(n<144100, c=0; a=prime(n); while(isprime(n*prime(n)+(n+1)*prime(n+1)), c++; n++); if(c==4, print1(a, ",")); n++)}

A152869 Beginnings of maximal chains of primes with six members (five links).

Original entry on oeis.org

417037, 736013, 1006007, 1563539, 13884217, 13893713, 20014021, 22037297, 22583789, 23496349, 26531251, 26864017, 27754471, 38767909, 41133299, 41383343, 43509359, 45085321, 48619393, 49243343, 51082139, 52754543
Offset: 1

Views

Author

Klaus Brockhaus, Dec 19 2008

Keywords

Comments

For definitions see A152658, of which this is a subsequence.

Examples

			First maximal chain of primes with six members (five links) is 417037, 417089, 417097, 417113, 417119, 417127; the five linking primes are 29322448367, 29325391741, 29327069663, 29328677311, 29330003749.

Links

Crossrefs

Cf. A152658 (beginnings of maximal chains of primes), A152735 (count of links in n-th maximal chain of primes), A152962 (beginning of the first maximal chain of primes with n links), A152865, A152866, A152867, A152868, A152963, A152964.

A152962 Beginning of the first maximal chain of primes with n links (n+1 members).

Original entry on oeis.org

29, 5, 13, 61, 417037, 2153, 4580041
Offset: 1

Views

Author

Klaus Brockhaus, Dec 16 2008

Keywords

Comments

For definitions see A152658.
The prime indices of the terms are 10, 3, 6, 18, 35153, 325, 321150.
Is this sequence finite, i.e. is the length (count of members) of chains of primes bounded?

Examples

			First maximal chain of primes with one link (two members) is 29, 31; the linking prime is 631.

Links

  • Carlos Rivera, The prime puzzles & problems connection, Puzzle 463

Crossrefs

Cf. A152658 (beginnings of maximal chains of primes), A152735 (count of links in n-th maximal chain of primes), A119487 (primes of the form i*(i-th prime) + (i+1)*((i+1)-th prime), linking primes), A152865, A152866, A152867, A152868, A152869, A152963, A152964.

A152963 Beginnings of maximal chains of primes with seven members (six links).

Original entry on oeis.org

2153, 10316897, 114286307, 220073429, 406733477
Offset: 1

Views

Author

Klaus Brockhaus, Dec 16 2008

Keywords

Comments

For definitions see A152658, of which this is a subsequence.

Examples

			First maximal chain of primes with seven members is 2153, 2161, 2179, 2203, 2207, 2213, 2221; the six linking primes are 1404211, 1417019, 1435117, 1448687, 1456393, 1465441.

Crossrefs

Cf. A152658 (beginnings of maximal chains of primes), A152962 (beginning of the first maximal chain of primes with n links), A152735 (count of links in n-th maximal chain of primes), A119487 (primes of the form i*(i-th prime) + (i+1)*((i+1)-th prime), linking primes), A152865, A152866, A152867, A152868, A152869, A152964.

A152964 Beginnings of maximal chains of primes with eight members (seven links).

Original entry on oeis.org

4580041, 608744947, 2784514741, 3336893489, 3743034679
Offset: 1

Views

Author

Klaus Brockhaus, Dec 16 2008

Keywords

Comments

For definitions see A152658, of which this is a subsequence.
Terms were computed by Farideh Firoozbakht (see C. Rivera link), who remarks that there are no other terms with prime indices up to 372*10^6, i.e., terms below approx. 8*10^9. The prime indices of the given terms are 321150, 31757516, 134558368, 159849354, 178323284.

Examples

			First maximal chain of primes with eight members is 4580041, 4580077, 4580117, 4580131, 4580141, 4580143, 4580201, 4580209; the seven linking primes are 2941776475777, 2941810043411, 2941836545827, 2941853413757, 2941866427879, 2941894857 521, 2941925214169.

Links

  • Carlos Rivera, The prime puzzles & problems connection, Puzzle 463

Crossrefs

Cf. A152962 (beginning of the first maximal chain of primes with n links), A152658 (beginnings of maximal chains of primes), A152735 (count of links in n-th maximal chain of primes), A119487 (primes of the form i*(i-th prime) + (i+1)*((i+1)-th prime), linking primes), A152865, A152866, A152867, A152868, A152869, A152963.
Showing 1-8 of 8 results.

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