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.

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A320706 Indices of primes followed by a gap (distance to next larger prime) of 16.

Original entry on oeis.org

282, 295, 319, 331, 335, 378, 409, 445, 476, 478, 481, 510, 560, 566, 619, 624, 674, 701, 739, 775, 856, 871, 881, 886, 935, 941, 1007, 1069, 1077, 1121, 1146, 1193, 1222, 1261, 1286, 1322, 1331, 1356, 1372, 1388, 1405, 1460, 1487, 1500, 1587, 1603, 1608, 1612, 1699, 1719, 1734, 1740, 1811, 1876, 1924, 1956, 1969, 1977, 2002, 2022, 2034, 2042, 2071
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A031934.

Links

Crossrefs

Equals A000720 o A031934.
Row 8 of A174349.
Indices of 16's in A001223.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

Formula

a(n) = A000720(A031934(n)).
A320706 = { i > 0 | prime(i+1) = prime(i) + 16 }.

A320707 Indices of primes followed by a gap (distance to next larger prime) of 18.

Original entry on oeis.org

99, 180, 205, 221, 274, 293, 326, 368, 416, 529, 539, 573, 597, 602, 607, 623, 635, 639, 677, 693, 725, 785, 811, 838, 844, 852, 855, 916, 937, 939, 942, 945, 968, 997, 1028, 1093, 1130, 1151, 1203, 1227, 1252, 1304, 1311, 1349, 1508, 1514, 1519, 1523, 1540, 1547, 1629, 1636, 1641, 1654, 1656
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A031936.

Links

Crossrefs

Equals A000720 o A031936.
Row 9 of A174349.
Indices of 18's in A001223.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • Magma
    [n: n in [1..1700] | NthPrime(n+1) - NthPrime(n) eq 18]; // Vincenzo Librandi, Mar 22 2019
  • Mathematica
    Select[Range[1700], Prime[#] + 18 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 22 2019 *)
Flatten[Position[Differences[Prime[Range[2000]]],18]] (* Harvey P. Dale, May 12 2022 *)
  • PARI
    A(N=100,g=18,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A031936(n)).
A320707 = { i > 0 | prime(i+1) = prime(i) + 18 } = A001223^(-1)({18}).

A320713 Indices of primes followed by a gap (distance to next larger prime) of 30.

Original entry on oeis.org

590, 650, 708, 757, 842, 890, 928, 985, 1006, 1051, 1108, 1556, 1570, 1648, 1650, 1675, 1754, 1900, 1919, 2027, 2125, 2149, 2321, 2391, 2397, 2429, 2631, 2637, 2699, 2781, 2866, 2918, 2989, 2993, 3010, 3085, 3153, 3207, 3315, 3340, 3350, 3373, 3420, 3511, 3551, 3580, 3637, 3751, 3777, 3948
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A124596.

Links

Crossrefs

Equals A000720 o A124596.
Indices of 30's in A001223.
Row 15 of A174349.
Subsequence of A107730 (prime(n+1) ends in same digit as prime(n)).
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • PARI
    A(N=100,g=30,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A124596(n)).
A320713 = { i>0 | prime(i+1) = prime(i) + 30 } = A001223^(-1)({30}).

A320718 Indices of primes followed by a gap (distance to next larger prime) of 40.

Original entry on oeis.org

2191, 2344, 2524, 2788, 3562, 4058, 4677, 5030, 5349, 6076, 6145, 6256, 6320, 6442, 6454, 6902, 7232, 7488, 8119, 8152, 8245, 8366, 8553, 8567, 8591, 8746, 9260, 9361, 10536, 10735, 11095, 11407, 11534, 11781, 12227, 12312, 12663, 12815, 12940, 13015, 13333, 13676, 13873, 14065, 14123
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A126721.

Links

Crossrefs

Equals A000720 o A126721.
Row 20 of A174349.
Subsequence of A107730 (prime(n+1) ends in same digit as prime(n)).
Indices of 40's in A001223.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • PARI
    A(N=100,g=40,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A126721(n)).
A320718 = { i > 0 | prime(i+1) = prime(i) + 40 } = A001223^(-1)({40}).

A320719 Indices of primes followed by a gap (distance to next larger prime) of 42.

Original entry on oeis.org

1879, 3732, 4059, 4135, 4714, 5355, 5948, 6160, 6841, 7434, 7724, 7746, 7952, 7980, 8081, 8269, 8580, 9303, 9395, 9971, 10045, 10305, 10968, 11023, 11135, 11251, 11338, 11399, 11515, 11807, 11888, 11901, 12089, 12374, 12488, 13277, 13447, 14497, 14802, 15086, 15089, 15350, 15612, 15785
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A134120.

Links

Crossrefs

Cf. A029707, A029709 (analog for gaps 2 & 4), A320701, A320702, ... A320720 (analog for gaps 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).
Equals A000720 o A134120.
Indices of 42's in A001223.
Row 21 of A174349.

Programs

  • Mathematica
    Position[Differences[Prime[Range[16000]]],42]//Flatten (* Harvey P. Dale, Feb 22 2020 *)
  • PARI
    A(N=100,g=42,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A134120(n)).

A320709 Indices of primes followed by a gap (distance to next larger prime) of 22.

Original entry on oeis.org

189, 297, 344, 375, 457, 487, 522, 549, 557, 721, 836, 914, 1010, 1158, 1170, 1197, 1233, 1242, 1272, 1290, 1370, 1390, 1444, 1471, 1625, 1633, 1672, 1683, 1757, 1858, 1975, 1983, 2039, 2074, 2158, 2243, 2248, 2250, 2327, 2370, 2388, 2614, 2638, 2703, 2725, 2838, 2842, 2872
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A061779.

Links

Crossrefs

Equals A000720 o A061779.
Row 11 of A174349.
Indices of 22's in A001223.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • Magma
    [n: n in [1..3000] | NthPrime(n+1) - NthPrime(n) eq 22]; // Vincenzo Librandi, Mar 22 2019
  • Mathematica
    Select[Range[3000], Prime[#] + 22 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 22 2019 *)
  • PARI
    A(N=100,g=22,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A061779(n)).
A320709 = { i > 0 | prime(i+1) = prime(i) + 22 }.

A320710 Indices of primes followed by a gap (distance to next larger prime) of 24.

Original entry on oeis.org

263, 327, 574, 615, 641, 697, 804, 834, 869, 909, 938, 987, 1022, 1045, 1127, 1336, 1399, 1421, 1446, 1452, 1551, 1577, 1865, 1883, 1908, 1938, 1939, 1968, 2032, 2064, 2128, 2130, 2176, 2214, 2313, 2508, 2555, 2592, 2612, 2652, 2736, 2762, 2991, 3162, 3243, 3285, 3483, 3489
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A098974.

Links

Crossrefs

Equals A000720 o A098974.
Row 12 of A174349.
Indices of 24's in A001223.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • Maple
    P:= [seq(ithprime(i),i=1..4001)]:
B:= P[2..-1]-P[1..-2]:
select(t -> B[t]=24, [$1..4000]); # Robert Israel, May 03 2019
  • PARI
    A(N=100,g=24,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A098974(n)).
A320710 = { i > 0 | prime(i+1) = prime(i) + 24 }.

A320711 Indices of primes followed by a gap (distance to next larger prime) of 26.

Original entry on oeis.org

367, 446, 732, 1357, 1440, 1475, 1746, 1864, 1912, 1933, 2293, 2714, 2888, 2912, 3159, 3204, 3362, 3523, 3715, 3786, 3801, 3840, 3870, 3920, 3931, 4107, 4164, 4235, 4240, 4502, 4643, 4809, 4957, 4990, 5110, 5371, 5440, 5451, 5581, 5712, 5736, 5743, 5870, 5882, 5906, 5923, 5933, 6018, 6277
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A124594.

Links

Crossrefs

Equals A000720 o A124594.
Row 13 of A174349.
Indices of 26's in A001223.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • PARI
    A(N=100,g=26,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A124594(n)).
A320711 = { i > 0 | prime(i+1) = prime(i) + 26 }.

A320712 Indices of primes followed by a gap (distance to next larger prime) of 28.

Original entry on oeis.org

429, 462, 685, 781, 1116, 1231, 1274, 1288, 1327, 1392, 1585, 1708, 1710, 1891, 1944, 2065, 2154, 2367, 2417, 2606, 2663, 2729, 2980, 3012, 3069, 3227, 3519, 3653, 3990, 4018, 4168, 4196, 4595, 4603, 4618, 4797, 4856, 4867, 5123, 5191, 5294, 5375, 5432, 5476, 5498, 5593, 5627, 5688, 5703
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A124595.

Links

Crossrefs

Equals A000720 o A124595.
Indices of 28's in A001223.
Row 14 of A174349.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • PARI
    A(N=100,g=28,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A124595(n)).
A320712 = { i > 0 | prime(i+1) = prime(i) + 28 }.

A320714 Indices of primes followed by a gap (distance to next larger prime) of 32.

Original entry on oeis.org

738, 1315, 3022, 3042, 3607, 4112, 4300, 4362, 4555, 4619, 4761, 4893, 5204, 5358, 5615, 5637, 6215, 6265, 6479, 6610, 6706, 6933, 7295, 7829, 7884, 8049, 8198, 8548, 9085, 9155, 9524, 9588, 9641, 9826, 9924, 10463, 10824, 11367, 11590, 11701, 11729, 11869, 12159, 12258, 12275, 12327
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A126784.

Links

Crossrefs

Equals A000720 o A126784.
Indices of 32's in A001223.
Row 16 of A174349.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • Maple
    p:= 2: Res:= NULL: count:= 0:
for k from 1 while count < 100 do
  q:= nextprime(p);
  if q - p = 32 then
    count:= count+1;
    Res:= Res, k;
  fi;
  p:= q;
od:
Res; # Robert Israel, Oct 25 2018
  • Mathematica
    PrimePi/@Select[Partition[Prime[Range[15000]],2,1],#[[2]]-#[[1]]==32&][[;;,1]] (* Harvey P. Dale, Jun 19 2024 *)
  • PARI
    A(N=100,g=32,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

Formula

a(n) = A000720(A126784(n)).
A320714 = { i>0 | prime(i+1) = prime(i) + 32 }.
Previous Showing 11-20 of 23 results. Next

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