A204189 -id:A204189 - cp's OEIS frontend

A261149 a(n) = 515486946529943 + (n-1)*30526020494970.

515486946529943, 546012967024913, 576538987519883, 607065008014853, 637591028509823, 668117049004793, 698643069499763, 729169089994733, 759695110489703, 790221130984673, 820747151479643, 851273171974613, 881799192469583, 912325212964553, 942851233459523

Offset: 1

Marco Ripà, Aug 10 2015

The terms n = 1..24 are prime. This is the longest known sequence of 24 primes in arithmetic progression with minimal end known as of August 10, 2015.

			a(24) = 515486946529943 + 23*30526020494970 = 1217585417914253 is prime.

Colin Barker, Table of n, a(n) for n = 1..1000
Jens Kruse Andersen, All known AP24 to AP26.
Wikipedia, Largest known primes in AP.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A005115, A002110, A204189.

[515486946529943+(n-1)*30526020494970: n in [1..20]];

Table[515486946529943 + (n - 1) 30526020494970, {n, 1, 20}]

Vec(-x*(484960926034973*x-515486946529943)/(x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

[515486946529943+(n-1)*30526020494970 for n in (1..20)] #

a(n) = 515486946529943 + (n-1)*136831*A002110(9).

G.f.: -x*(484960926034973*x-515486946529943) / (x-1)^2. - Colin Barker, Aug 25 2015

A261150 a(n) = 403185216600637 + (n-1)*2124513401010.

Original entry on oeis.org

403185216600637, 405309730001647, 407434243402657, 409558756803667, 411683270204677, 413807783605687, 415932297006697, 418056810407707, 420181323808717, 422305837209727, 424430350610737, 426554864011747, 428679377412757, 430803890813767, 432928404214777

Offset: 1

Marco Ripà, Aug 10 2015

The terms n = 1..23 are prime. This is the longest known sequence of 23 primes in arithmetic progression with minimal end known as of August 10, 2015.

			a(23) = 403185216600637 + 22*2124513401010 = 449924511422857 is prime.

Colin Barker, Table of n, a(n) for n = 1..1000
Jens Kruse Andersen, All known AP24 to AP26.
Wikipedia, Largest known primes in AP.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A005115, A002110, A204189.

[403185216600637+(n-1)*2124513401010: n in [1..20]];

Table[403185216600637 + (n - 1) 2124513401010, {n, 1, 23}]

Vec(-x*(401060703199627*x-403185216600637)/(x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

[403185216600637+(n-1)*2124513401010 for n in (1..20)]

a(n) = 403185216600637 + (n-1)*9523*A002110(9).

G.f.: -x*(401060703199627*x-403185216600637) / (x-1)^2. - Colin Barker, Aug 25 2015

A261151 a(n) = 11410337850553 + (n-1)*4609098694200.

Original entry on oeis.org

11410337850553, 11871247719973, 12332157589393, 12793067458813, 13253977328233, 13714887197653, 14175797067073, 14636706936493, 15097616805913, 15558526675333, 16019436544753, 16480346414173, 16941256283593, 17402166153013, 17863076022433, 18323985891853

Offset: 1

Marco Ripà, Aug 10 2015

The terms n = 1..22 are prime. This is the longest known sequence of 22 primes in arithmetic progression with minimal end known as of August 10, 2015.

			a(22) = 11410337850553 + 21*4609098694200 = 108201410428753 is prime.

Colin Barker, Table of n, a(n) for n = 1..1000
Jens Kruse Andersen, All known AP24 to AP26.
Wikipedia, Largest known primes in AP.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A005115, A002110, A204189.

[11410337850553+(n-1)*4609098694200: n in [1..20]];

Table[11410337850553 + (n - 1) 4609098694200, {n, 1, 20}]

Vec(-x*(10949427981133*x-11410337850553) / (x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

[11410337850553+(n-1)*4609098694200 for n in (1..20)]

a(n) = 11410337850553 + (n-1)*475180*A002110(8).

G.f.: -x*(10949427981133*x-11410337850553) / (x-1)^2. - Colin Barker, Aug 25 2015

A261152 a(n) = 161004359399459161 + (n-1)*10644900609172830.

Original entry on oeis.org

161004359399459161, 171649260008631991, 182294160617804821, 192939061226977651, 203583961836150481, 214228862445323311, 224873763054496141, 235518663663668971, 246163564272841801, 256808464882014631, 267453365491187461, 278098266100360291, 288743166709533121

Offset: 1

Marco Ripà, Aug 10 2015

The terms n = 1..26 are prime. This is the longest and largest sequence of primes in arithmetic progression, a(26)=427126874628779911, known as of August 10, 2015.

			a(26) = 161004359399459161 + 25*10644900609172830 = 427126874628779911 is prime.

Jens Kruse Andersen, All known AP24 to AP26.
Wikipedia, Largest known primes in AP.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A002110, A204189, A260751.

[161004359399459161+(n-1)*10644900609172830: n in [1..20]]; // Bruno Berselli, Aug 23 2015

Table[161004359399459161 + (n - 1) 10644900609172830, {n, 1, 20}] (* Bruno Berselli, Aug 23 2015 *)

a(n) = 161004359399459161 + (n-1)*47715109*A002110(9).

G.f.: x*(161004359399459161 - 150359458790286331*x)/(1 - x)^2. [Bruno Berselli, Aug 23 2015]

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

A261149 a(n) = 515486946529943 + (n-1)*30526020494970.

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A261150 a(n) = 403185216600637 + (n-1)*2124513401010.

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A261151 a(n) = 11410337850553 + (n-1)*4609098694200.

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A261152 a(n) = 161004359399459161 + (n-1)*10644900609172830.

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

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

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