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 1-6 of 6 results.

A227284 First primes of arithmetic progressions of 9 primes each with the common difference 210.

Original entry on oeis.org

199, 409, 3499, 10859, 564973, 1288607, 1302281, 2358841, 3600521, 4047803, 17160749, 20751193, 23241473, 44687567, 50655739, 53235151, 87662609, 100174043, 103468003, 110094161, 180885839, 187874017, 192205147, 221712811, 243051733, 243051943, 304570103
Offset: 1

Views

Author

Sameen Ahmed Khan, Jul 05 2013

Keywords

Comments

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.
When a(n+1) = a(n) + 210, as for n = 1, 25, ..., then a(n) is in A094220: start of AP of 10 primes with common distance 210. - M. F. Hasler, Jan 02 2020

Examples

			p = 409 then the AP-9 is {409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089} with the difference 9# = 2*3*5*7 = 210.

Links

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227285, A227286.

Programs

  • Mathematica
    Clear[p]; d = 210; ap9p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d}] == {True, True, True, True, True, True, True, True, True}, AppendTo[ap9p, p]], {p, 3, 10^9, 2}]; ap9p
  • PARI
    v=[1..8]*210; forprime(p=1,,for(i=1,#v,isprime(p+v[i])||next(2));print1(p",")) \\ M. F. Hasler, Jan 02 2020

A156204 First primes of an arithmetic progression of six primes with common difference 30.

Original entry on oeis.org

7, 107, 359, 541, 2221, 6673, 7457, 10103, 25643, 26861, 27337, 35051, 56149, 61553, 65557, 73523, 84317, 110819, 115733, 131581, 135151, 137447, 179321, 228587, 243553, 252163, 279421, 281717, 310711, 320119, 337367, 345487, 347167, 357079
Offset: 1

Views

Author

Ki Punches, Feb 05 2009

Keywords

Comments

Subsequence of A155760. - R. J. Mathar, Feb 07 2009
After the first term, all terms are congruent to 9 (mod 14). Gaps of 14 occur at a(n) = 22037759, 400852853, ... - Zak Seidov, Aug 01 2013
Subsequence of A227281. - Zak Seidov, Aug 26 2014
Note that a(n)+6*30 is composite for all n: a(1)+180 is divisible by 11 and for n>1 a(n)+180 is divisible by 7. - Zak Seidov, Apr 11 2015

Links

Crossrefs

Cf. A155760, A227281.

Programs

  • Magma
    [p: p in PrimesUpTo(360000)| IsPrime(p+30) and IsPrime(p+60) and IsPrime(p+90)and IsPrime(p+120)and IsPrime(p+150)]; // Vincenzo Librandi, Apr 13 2015
  • Maple
    for n from 1 to 60000 do p := ithprime(n) ; if isprime(p+30) and isprime(p+60) and isprime(p+90) and isprime(p+120) and isprime(p+150) then printf("%d,",p) ; fi; od: # R. J. Mathar, Feb 07 2009
  • Mathematica
    Select[Range[360000], PrimeQ[#] && PrimeQ[# + 30] && PrimeQ[# + 60] && PrimeQ[# + 90] && PrimeQ[# + 120] && PrimeQ[# + 150] &] (* Vincenzo Librandi, Apr 13 2015 *)
  • PARI
    is_A156204(n) = isprime(n) && isprime(n+30) && isprime(n+60) && isprime(n+90) && isprime(n+120) && isprime(n+150) \\ Michael B. Porter, Aug 01 2013

Extensions

Corrected and extended by R. J. Mathar and Ray Chandler, Feb 08 2009

A227282 First primes of arithmetic progressions of 7 primes each with the common difference 210.

Original entry on oeis.org

47, 179, 199, 409, 619, 829, 881, 1091, 1453, 3499, 3709, 3919, 10529, 10627, 10837, 10859, 11069, 11279, 14423, 20771, 22697, 30097, 30307, 31583, 31793, 32363, 41669, 75703, 93281, 95747, 120661, 120737, 120871, 120947, 129287, 140603, 153319, 153529
Offset: 1

Views

Author

Sameen Ahmed Khan, Jul 05 2013

Keywords

Comments

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.
For k = 7, we have d = 5*5# = 150 and there is ONLY one AP-7 with this difference: {7, 157, 307, 457, 607, 757, 907}.

Examples

			p = 179 then the AP-5 is {179, 389, 599, 809, 1019, 1229, 1439} with the difference 7# = 210.

Links

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227283, A227284, A227285, A227286.

Programs

  • Mathematica
    Clear[p]; d = 210; ap7p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d}] == {True, True, True, True, True, True, True}, AppendTo[ap7p, p]], {p, 3, 10^9, 2}]; ap7p
Select[Prime[Range[15000]],And@@PrimeQ[NestList[210+#&,#,6]]&] (* Harvey P. Dale, Nov 16 2013 *)
  • PARI
    is(p)=forstep(k=p,p+1260,210,if(!isprime(k),return(0)));1 \\ Charles R Greathouse IV, Dec 19 2013

A227283 First primes of arithmetic progressions of 8 primes each with the common difference 210.

Original entry on oeis.org

199, 409, 619, 881, 3499, 3709, 10627, 10859, 11069, 30097, 31583, 120661, 120737, 153319, 182537, 471089, 487391, 564973, 565183, 825991, 1010747, 1280623, 1288607, 1288817, 1302281, 1302491, 1395209, 1982599, 2358841, 2359051, 2439571, 3161017, 3600521
Offset: 1

Views

Author

Sameen Ahmed Khan, Jul 05 2013

Keywords

Comments

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.

Links

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227284, A227285, A227286.

Programs

  • Mathematica
    Clear[p]; d = 210; ap8p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d}] == {True, True, True, True, True, True, True, True}, AppendTo[ap8p, p]], {p, 3, 3000000, 2}]; ap8p
Select[Prime[Range[260000]],AllTrue[NestList[#+210&,#,7],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 03 2018 *)

A227285 First primes of arithmetic progressions of 11 primes each with the common difference 2310.

Original entry on oeis.org

60858179, 186874511, 291297353, 1445838451, 2943023729, 4597225889, 7024895393, 8620560607, 8656181357, 19033631401, 20711172773, 25366690189, 27187846201, 32022299977, 34351919351
Offset: 1

Views

Author

Sameen Ahmed Khan, Jul 05 2013

Keywords

Comments

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.
16th term is greater than 40*10^9.

Examples

			p = 186874511 then the AP-11 is {186874511, 186876821, 186879131, 186881441, 186883751, 186886061, 186888371, 186890681, 186892991, 186895301, 186897611} with the difference 11# = 2*3*5*7*11 = 2310.

Links

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227284, A227286.

Programs

  • Mathematica
    Clear[p]; d = 2310; ap11p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d, p + 9*d, p + 10*d}] == {True, True, True, True, True, True, True, True, True, True, True}, AppendTo[ap11p, p]], {p, 3, 40*10^9, 2}]; ap11p
ap11Q[n_]:=AllTrue[Rest[NestList[2310+#&,n,10]],PrimeQ]; Select[Prime[ Range[ 148*10^7]],ap11Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* The program will take a long time to run *) (* Harvey P. Dale, Oct 27 2019 *)

Extensions

a(16)-a(21) from Zak Seidov, Jul 07 2014

A227286 First primes of arithmetic progressions of 13 primes each with the common difference 30030.

Original entry on oeis.org

14933623, 2085471361, 132420258931, 185041386139, 682539280751, 834172298383, 834172328413, 856378247603, 856378277633, 888867525577, 931115864233, 1059709587163, 1345030977911, 1360910561113, 1578280523803, 1973348047529, 1988253536611, 2083502941613
Offset: 1

Views

Author

Sameen Ahmed Khan, Jul 05 2013

Keywords

Comments

The minimal possible difference in an arithmetic progression of k primes is conjectured to be k# = A034386(k) for all k > 7. 13# = 30030.

Examples

			p = 2085471361 then the AP-13 is {2085471361, 2085501391, 2085531421, 2085561451, 2085591481, 2085621511, 2085651541, 2085681571, 2085711601, 2085741631, 2085771661, 2085801691, 2085831721} with the difference 13# = 2*3*5*7*11*13 = 30030.

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227284, A227285.

Programs

  • Mathematica
    Clear[p]; d = 30030; ap13p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d, p + 9*d, p + 10*d, p + 11*d, p + 12*d}] == {True, True, True, True, True, True, True, True, True, True, True, True, True}, AppendTo[ap13p, p]], {p, 3, 41*10^9, 2}]; ap13p

Extensions

More terms from Jens Kruse Andersen, Jun 27 2014
Showing 1-6 of 6 results.

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