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.

User: Alexander Yutkin

Alexander Yutkin's wiki page.

Alexander Yutkin has authored 15 sequences. Here are the ten most recent ones:

A385824 Primes p such that p + 10, p + 18, p + 24, p + 28 and p + 30 are also primes.

Original entry on oeis.org

13, 43, 79, 14533, 41203, 42433, 47119, 88789, 113143, 150193, 340909, 348433, 416389, 556243, 576193, 609589, 626599, 637699, 669649, 715849, 752263, 855709, 859249, 891799, 1107763, 1146763, 1189603, 1191079, 1201999, 1210369, 1225099, 1416043, 1510189, 1601599, 1893163
Offset: 1

Views

Author

Alexander Yutkin, Jul 09 2025

Keywords

Comments

Initial members of prime sextuples that correspond to the difference pattern [10, 8, 6, 4, 2]. The primes in a sextuple do not have to be consecutive.

Examples

			p=13: 13+10=23, 13+18=31, 13+24=37, 13+28=41, 13+30=43 —> prime sextuple: (13, 23, 31, 37, 41, 43).

Crossrefs

Cf. A000040.
Cf. A187057 [2, 4, 6, 8], A385035 [8, 6, 4, 2], A187058 [2, 4, 6, 8, 10].

Programs

  • Mathematica
    Select[Prime[Range[150000]], And @@ PrimeQ[# + {10, 18, 24, 28, 30}] &] (* Amiram Eldar, Jul 09 2025 *)

A385035 Primes p such that p + 8, p + 14, p + 18 and p + 20 are also primes.

Original entry on oeis.org

23, 53, 89, 263, 599, 1283, 1979, 3449, 5399, 5639, 11813, 14543, 41213, 42443, 44249, 47129, 55799, 57773, 65699, 74699, 75983, 79613, 84299, 87539, 88643, 88793, 88799, 113153, 115763, 126473, 143813, 148913, 150203, 160073, 163973, 167099, 176489, 178799, 178889, 209249
Offset: 1

Views

Author

Alexander Yutkin, Jun 15 2025

Keywords

Examples

			p=23: 23+8=31, 23+14=37, 23+18=41, 23+20=43 —> prime quintuple: (23, 31, 37, 41, 43).

Crossrefs

Cf. A000040.
Cf. A172454 [2, 4, 6], A078855 [6, 4, 2], A187057 [2, 4, 6, 8].

Programs

  • Magma
    [p: p in PrimesUpTo(300000) | IsPrime(p+8) and IsPrime(p+14) and IsPrime(p+18) and IsPrime(p+20)]; // Vincenzo Librandi, Jul 04 2025
  • Maple
    q:= p-> andmap(i-> isprime(p+i), [0, 8, 14, 18, 20]):
select(q, [5+6*i$i=0..35000])[];  # Alois P. Heinz, Jun 16 2025
  • Mathematica
    Select[Prime[Range[20000]], AllTrue[#+{8, 14, 18,20}, PrimeQ]&] (* Stefano Spezia, Jun 18 2025 *)

A385201 Palindromic primes indexed by palindromic primes.

Original entry on oeis.org

3, 5, 11, 131, 313, 94349, 1123211, 1212121, 1360631, 1422241, 3075703, 3293923, 3400043, 3447443, 9711179, 9852589, 100161001, 101171101, 108505801, 109111901, 13929592931, 14125852141, 14209390241, 14895559841, 14986568941, 15911711951, 16172327161, 16257475261, 16727672761
Offset: 1

Views

Author

Alexander Yutkin, Jun 21 2025

Keywords

Examples

			a(3) = 11 because a(3) = A002385(A002385(3)) = A002385(5) = 11.

Crossrefs

Subsequence of A002385.
Cf. A000040, A002113.

Formula

a(n) = A002385(A002385(n)).

A384769 Primes p such that p + 6, p + 12, p + 20, p + 26 and p + 32 are also primes.

Original entry on oeis.org

11, 41, 47, 251, 347, 587, 1097, 1427, 2687, 5387, 11801, 17021, 19457, 23741, 24071, 32057, 42677, 47501, 55787, 55817, 71327, 115751, 127637, 165437, 179801, 191441, 226637, 282671, 344231, 344237, 348431, 349907, 391367, 408197, 411557, 416387, 422057, 501197, 526931, 571841, 572801
Offset: 1

Views

Author

Alexander Yutkin, Jun 09 2025

Keywords

Comments

Initial members of prime sextuples that correspond to the difference pattern [6, 6, 8, 6, 6].

Examples

			p=47: 47+6=53, 47+12=59, 47+20=67, 47+26=73, 47+32=79 —> prime sextuple: (47, 53, 59, 67, 73, 79).

Crossrefs

Cf. A000040, A001223.
Cf. A384526 [6, 8, 6], A384527 [6, 6, 2, 6, 6], A384528 [6, 6, 4, 6, 6].

Programs

  • Mathematica
    Select[Prime[Range[50000]], AllTrue[#+{6, 12, 20, 26, 32}, PrimeQ]&] (* Stefano Spezia, Jun 09 2025 *)

A384771 Primes p such that p + 8, p + 12, p + 20, p + 24 and p + 32 are also primes.

Original entry on oeis.org

58889, 114749, 185519, 476579, 568979, 904769, 1726919, 4143389, 4413029, 6432599, 7571009, 9848249, 10444859, 12271439, 12338849, 13599689, 14669639, 15136259, 16390799, 17016809, 18453209, 20649809, 22190579, 22581809, 23475359, 24249419, 26979419, 29202059, 30126269, 30869669, 33263039
Offset: 1

Views

Author

Alexander Yutkin, Jun 09 2025

Keywords

Comments

Initial members of prime sextuples that correspond to the difference pattern [8, 4, 8, 4, 8].

Examples

			p=58889: 58889+8=58897, 58889+12=58901, 58889+20=58909, 58889+24=58913, 58889+32=58921 —> prime sextuple: (58889, 58897, 58901, 58909, 58913, 58921).

Crossrefs

Cf. A000040, A001223.
Cf. A384298 [4, 8, 4], A384299 [8, 4, 8], A022008 [4, 2, 4, 2, 4].

Programs

  • Mathematica
    Select[Prime[Range[2100000]], AllTrue[#+{8, 12, 20, 24, 32}, PrimeQ]&] (* Stefano Spezia, Jun 09 2025 *)

Formula

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

A384526 Primes p such that p + 6, p + 14 and p + 20 are also primes.

Original entry on oeis.org

17, 23, 47, 53, 83, 257, 263, 353, 443, 557, 587, 593, 977, 1103, 1217, 1277, 1283, 1433, 1607, 1973, 1997, 2267, 2657, 2693, 2837, 3527, 3617, 4007, 4637, 4643, 4937, 5393, 5807, 6197, 6257, 6323, 6353, 6977, 8693, 10253, 10847, 10973, 11483, 11807, 12143, 12497, 12953, 13613, 14537
Offset: 1

Views

Author

Alexander Yutkin, Jun 01 2025

Keywords

Comments

Initial members of prime quartets that correspond to the difference pattern [6, 8, 6].

Examples

			p=47: 47+6=53, 47+14=61, 47+20=67 —> prime quartet: (47, 53, 61, 67).

Crossrefs

Cf. A000040, A001223.
Cf. A140565 [6, 2, 6], A382810 [6, 4, 6].

Programs

  • Maple
    select(p -> andmap(isprime,[p, p + 6, p + 14, p + 20]), [seq(i,i=5 .. 20000, 6)]); # Robert Israel, Jun 01 2025
  • Mathematica
    Select[Prime[Range[1700]], PrimeQ[#+6]&&PrimeQ[#+14]&&PrimeQ[#+20] &] (* Stefano Spezia, Jun 01 2025 *)

Formula

a(n) == 5 (mod 6). - Hugo Pfoertner, Jun 01 2025

A384527 Primes p such that p + 6, p + 12, p + 14, p + 20 and p + 26 are also primes.

Original entry on oeis.org

17, 47, 257, 587, 1277, 4637, 14537, 19457, 71327, 101267, 113147, 115757, 150197, 179807, 191447, 193367, 267887, 302567, 344237, 408197, 416387, 442817, 482387, 536267, 566537, 652727, 886967, 1043747, 1268777, 1300127, 1373147, 1464257, 1589657, 1616597, 1988237
Offset: 1

Views

Author

Alexander Yutkin, Jun 01 2025

Keywords

Comments

Initial members of prime sextuples that correspond to the difference pattern [6, 6, 2, 6, 6].

Examples

			p=257: 257+6=263, 257+12=269, 257+14=271, 257+20=277, 257+26=283 —> prime sextuple: (257, 263, 269, 271, 277, 283).

Crossrefs

Cf. A000040, A001223.
Cf. A023241 [6, 6], A140565 [6, 2, 6].

Programs

  • Mathematica
    Select[Prime[Range[150000]],PrimeQ[#+6]&&PrimeQ[#+12]&&PrimeQ[#+14]&&PrimeQ[#+20]&&PrimeQ[#+26] &] (* Stefano Spezia, Jun 01 2025 *)

Formula

a(n) == 17 (mod 30). - Hugo Pfoertner, Jun 01 2025

A384528 Primes p such that p + 6, p + 12, p + 16, p + 22 and p + 28 are also primes.

Original entry on oeis.org

31, 151, 2671, 20101, 128461, 198811, 297601, 307261, 350431, 354301, 531331, 560221, 585721, 649771, 813991, 1049821, 1141081, 1553401, 1616611, 1763401, 2032621, 2126611, 2349301, 2628811, 2874721, 2967331, 3014371, 3414211, 3441931, 3491071, 3677341, 3699181, 4192261, 4941241, 4951621
Offset: 1

Views

Author

Alexander Yutkin, Jun 01 2025

Keywords

Comments

Initial members of prime sextuples that correspond to the difference pattern [6, 6, 4, 6, 6].

Examples

			p=151: 151+6=157, 151+12=163, 151+16=167, 151+22=173, 151+28=179 —> prime sextuple: (151, 157, 163, 167, 173, 179).

Crossrefs

Cf. A000040, A001223.
Cf. A023241 [6, 6], A382810 [6, 4, 6].

Programs

  • Mathematica
    Select[Prime[Range[350000]],PrimeQ[#+6]&&PrimeQ[#+12]&&PrimeQ[#+16]&&PrimeQ[#+22]&&PrimeQ[#+28] &] (* Stefano Spezia, Jun 01 2025 *)

Formula

a(n) == 1 (mod 30). - Hugo Pfoertner, Jun 01 2025

A384298 Primes p such that p + 4, p + 12 and p + 16 are also primes.

Original entry on oeis.org

7, 67, 97, 487, 757, 1567, 1597, 2377, 3907, 7687, 8677, 12097, 12907, 13147, 14407, 14767, 15667, 16057, 19417, 21487, 31177, 38317, 43777, 52567, 57637, 58897, 65167, 65827, 67477, 67927, 74857, 81547, 90007, 90187, 93967, 94777, 95467, 95617, 102547, 111427, 112237, 114757, 123817, 129277
Offset: 1

Views

Author

Alexander Yutkin, May 25 2025

Keywords

Comments

Initial members of prime quartets that correspond to the difference pattern [4, 8, 4].

Examples

			p=97: 97+4=101, 97+12=109, 97+16=113 —> prime quartet: (97, 101, 109, 113).

Links

Crossrefs

Cf. A000040, A001223.
Cf. A136162 [2, 4, 2], A052378 [4, 2, 4], A382810 [6, 4, 6].

Programs

  • Maple
    q:= n-> andmap(i-> isprime(n+4*i), [0,1,3,4]):
select(q, [7+30*i$i=0..4309])[];  # Alois P. Heinz, May 29 2025
  • Mathematica
    Select[Prime[Range[12099]],AllTrue[#+{4,12,16},PrimeQ]&] (* James C. McMahon, May 29 2025 *)

Formula

a(n) == 7 (mod 30).

A384299 Primes p such that p + 8, p + 12 and p + 20 are also primes.

Original entry on oeis.org

11, 59, 89, 389, 479, 1439, 1559, 1601, 2531, 2699, 3209, 3449, 3911, 5639, 5849, 7529, 8081, 8669, 10091, 12269, 12401, 12899, 13151, 14411, 14759, 17021, 19421, 21011, 21851, 22271, 23189, 25931, 26099, 28649, 28859, 31139, 31469, 33191, 33569, 36551, 39659, 40751, 42689, 43391, 43781, 44111
Offset: 1

Views

Author

Alexander Yutkin, May 25 2025

Keywords

Comments

Initial members of prime quartets that correspond to the difference pattern [8, 4, 8].

Examples

			p=89: 89+8=97, 89+12=101, 89+20=109 —> prime quartet: (89, 97, 101, 109).

Crossrefs

Cf. A000040, A001223.
Cf. A136162 [2, 4, 2], A052378 [4, 2, 4], A382810 [6, 4, 6].

Programs

  • Maple
    q:= n-> andmap(i-> isprime(n+4*i), [0,2,3,5]):
select(q, [5+6*i$i=1..7351])[];  # Alois P. Heinz, May 29 2025
  • Mathematica
    Select[Prime[Range[4591]],AllTrue[#+{8,12,20},PrimeQ]&] (* James C. McMahon, May 29 2025 *)

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