A317163 -id:A317163 - cp's OEIS frontend

A317164 a(n) = 55837783597462913 + (n-1)*13858932213216090.

55837783597462913, 69696715810679003, 83555648023895093, 97414580237111183, 111273512450327273, 125132444663543363, 138991376876759453, 152850309089975543, 166709241303191633, 180568173516407723, 194427105729623813, 208286037942839903, 222144970156055993

Offset: 1

Marco Ripà, Jul 23 2018

The terms for n = 1..26 are prime. As of Jul 23 2018, this is one of the longest known sequences of primes in arithmetic progression.

			a(26) = 55837783597462913 + 25*62121807*223092870 = 402311088927865163 is prime.

Jens Kruse Andersen, All known AP24 to AP26.
B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), 481-547.
PrimeGrid, AP26 Search.
Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
Wikipedia, Primes in arithmetic progression.

Cf. A002110, A204189, A260751, A261140, A317163.

List([1..25],n->55837783597462913+(n-1)*13858932213216090); # Muniru A Asiru, Jul 24 2018

seq(55837783597462913+(n-1)*13858932213216090,n=1..15); # Muniru A Asiru, Jul 24 2018

Table[55837783597462913 + (n - 1) 13858932213216090, {n, 1, 25}]

a(n) = 455837783597462913 + a(n-1)*62121807*23#, where 23# := 2*3*5*7*11*13*17*19*23 = 223092870.

A317255 a(n) = 149836681069944461 + (n-1)*1723457117682300.

Original entry on oeis.org

149836681069944461, 151560138187626761, 153283595305309061, 155007052422991361, 156730509540673661, 158453966658355961, 160177423776038261, 161900880893720561, 163624338011402861, 165347795129085161, 167071252246767461, 168794709364449761, 170518166482132061

Offset: 1

Marco Ripà, Jul 25 2018

The terms for n = 1..26 are prime. As of Jul 25 2018, this is one of the longest known sequences of primes in arithmetic progression.

			a(26) = 149836681069944461 + 25*7725290*223092870 = 192923109012001961 is prime.

Jens Kruse Andersen, All known AP24 to AP26.
B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), 481-547.
PrimeGrid, AP26 Search.
Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
Wikipedia, Primes in arithmetic progression.

Cf. A002120, A204189, A260751, A261140, A317163, A317164.

List([1..25], n->149836681069944461+(n-1)*1723457117682300);

seq(149836681069944461+(n-1)*1723457117682300,n=1..25);

Table[149836681069944461 + (n - 1) 1723457117682300, {n, 1, 25}]

A317259 a(n) = 136926916457315893 + (n - 1)*9843204333812850.

Original entry on oeis.org

136926916457315893, 146770120791128743, 156613325124941593, 166456529458754443, 176299733792567293, 186142938126380143, 195986142460192993, 205829346794005843, 215672551127818693, 225515755461631543, 235358959795444393, 245202164129257243, 255045368463070093

Offset: 1

Marco Ripà, Jul 25 2018

The terms for n = 1..26 are prime. As of Jul 25 2018, this is one of the longest known sequences of primes in arithmetic progression.
a(27) = 392850229136449993 = 41 * 179 * 53529122378587.
To date, an arithmetic sequence of 27 primes has not been found yet.

			a(26) = 136926916457315893 + 25*44121555*223092870 = 383007024802637143 is prime.

Jens Kruse Andersen, All known AP24 to AP26.
B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), 481-547.
PrimeGrid, AP26 Search.
Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
Wikipedia, Primes in arithmetic progression.

Cf. A002120, A204189, A260751, A261140, A317163, A317164.

List([1..25], n->136926916457315893+(n-1)*9843204333812850);

seq(136926916457315893+(n-1)*9843204333812850,n=1..25);

Table[136926916457315893 + (n - 1) 9843204333812850, {n, 1, 25}]

a(7) corrected by Georg Fischer, Mar 13 2020

A317914 a(n) = 142099325379199423 + (n-1)*3691994023167450.

Original entry on oeis.org

142099325379199423, 145791319402366873, 149483313425534323, 153175307448701773, 156867301471869223, 160559295495036673, 164251289518204123, 167943283541371573, 171635277564539023, 175327271587706473, 179019265610873923

Offset: 1

Marco Ripà, Aug 10 2018

The terms for n = 1..26 are prime. As of Aug 10 2018, this is one of the longest known sequences of primes in arithmetic progression.

			a(26) = 142099325379199423 + 25*16549135*223092870 = 234399175958385673 is prime.

Jens Kruse Andersen, All known AP24 to AP26.
B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), 481-547.
PrimeGrid, AP26 Search.
Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
Wikipedia, Primes in arithmetic progression.

Cf. A002110, A204189, A260751, A261140, A317163, A317164.

List([1..26],n->142099325379199423+(n-1)*3691994023167450);

seq(142099325379199423+(n-1)*3691994023167450,n=1..26);

Table[142099325379199423 + (n - 1) 3691994023167450, {n, 1, 26}]

a(n) = 142099325379199423 + a(n-1)*16549135*23#, where 23# := 2*3*5*7*11*13*17*19*23 = 223092870.

cp's OEIS Frontend

A317164 a(n) = 55837783597462913 + (n-1)*13858932213216090.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Maple

Mathematica

Formula

A317255 a(n) = 149836681069944461 + (n-1)*1723457117682300.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Maple

Mathematica

A317259 a(n) = 136926916457315893 + (n - 1)*9843204333812850.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Maple

Mathematica

Extensions

A317914 a(n) = 142099325379199423 + (n-1)*3691994023167450.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Maple

Mathematica

Formula