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 1-10 of 20 results. Next

A320701 Indices of primes followed by a gap (distance to next larger prime) of 6.

Original entry on oeis.org

9, 11, 15, 16, 18, 21, 23, 32, 36, 37, 39, 40, 51, 54, 55, 56, 58, 67, 71, 73, 74, 76, 84, 86, 96, 100, 102, 103, 105, 107, 108, 110, 111, 118, 119, 123, 129, 130, 133, 160, 161, 164, 165, 167, 170, 174, 179, 184, 185, 187, 188, 194, 195, 199, 200, 202, 208, 210, 216, 218, 219, 227, 231
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes given in A031924.
Subsequence of indices of sexy primes A023201.

Links

Crossrefs

Equals A000720 o A031924.
Row 3 of A174349.
Indices of 6's in A001223.
Cf. A029707, A029709, A320702, A320703, ..., A320720 (analog for gaps 2, 4, 8, 10, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

  • Mathematica
    Position[Differences[Prime[Range[250]]],6]//Flatten (* Harvey P. Dale, Oct 13 2022 *)
  • PARI
    A(N=100,g=6,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(A031924(n)).
A320701 = { i > 0 | prime(i+1) = prime(i) + 6 } = A001223^(-1)({6}).

A320720 Indices of primes followed by a gap (distance to next larger prime) of 44.

Original entry on oeis.org

1831, 3861, 4009, 7499, 8937, 10328, 10427, 11725, 12904, 12926, 13011, 13051, 16596, 16915, 18280, 20055, 20160, 20352, 20619, 21458, 21465, 21550, 21659, 23752, 23934, 24107, 24384, 24445, 24651, 24871, 24933, 24992, 25027, 26089, 26166, 26483, 26923, 27038, 27048, 28898, 29343
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A134121.

Links

Crossrefs

Cf. A029707, A029709 (analog for gaps 2 and 4), A320701, A320702, ... A320719 (analog for gaps 6, 8, 10, ..., 42), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).
Equals A000720 o A134121.
Indices of 44's in A001223.
Row 22 of A174349.

Programs

  • PARI
    A(N=100,g=44,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(A134121(n)).

A320703 Indices of primes followed by a gap (distance to next larger prime) of 10.

Original entry on oeis.org

34, 42, 53, 61, 68, 80, 82, 101, 106, 115, 125, 127, 138, 141, 145, 157, 172, 175, 177, 191, 193, 204, 222, 233, 258, 266, 269, 279, 289, 306, 308, 310, 316, 324, 369, 383, 397, 399, 403, 418, 422, 431, 443, 474, 491, 497, 500, 502, 518, 525, 531, 535, 575
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes given in A031928.

Links

Crossrefs

Equals A000720 o A031928.
Row 5 of A174349.
Indices of 10's in A001223.
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

Formula

a(n) = A000720(A031928(n)).
A320703 = { i > 0 | prime(i+1) = prime(i) + 10 }.

A320708 Indices of primes followed by a gap (distance to next larger prime) of 20.

Original entry on oeis.org

154, 259, 442, 480, 548, 753, 777, 783, 876, 971, 1035, 1066, 1095, 1106, 1147, 1254, 1277, 1302, 1337, 1345, 1355, 1381, 1396, 1400, 1423, 1438, 1562, 1592, 1613, 1662, 1669, 1808, 1955, 2016, 2043, 2081, 2116, 2129, 2147, 2226, 2302, 2307, 2387, 2517, 2547, 2563, 2694, 2724, 2745, 2755, 2766
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A031938.

Links

Crossrefs

Equals A000720 o A031938.
Row 10 of A174349.
Subsequence of A107730 (prime(n+1) ends in same digit as prime(n)).
Indices of 20'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 20]; // Vincenzo Librandi, Mar 22 2019
  • Mathematica
    Select[Range[3000], Prime[#] + 20 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 22 2019 *)
  • PARI
    A(N=100,g=20,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(A031938(n)).
A320708 = { i > 0 | prime(i+1) = prime(i) + 20 } = A001223^(-1)({20}).

A320704 Indices of primes followed by a gap (distance to next larger prime) of 12.

Original entry on oeis.org

46, 47, 91, 97, 114, 121, 139, 168, 197, 203, 214, 232, 239, 240, 242, 267, 278, 280, 290, 312, 317, 342, 357, 363, 376, 381, 404, 423, 437, 439, 449, 452, 461, 470, 472, 489, 499, 511, 546, 550, 562, 565, 599, 600, 617, 633, 634, 647, 653, 657, 675, 680, 692, 698, 716, 728
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes given in A031930.

Links

Crossrefs

Equals A000720 o A031930.
Row 6 of A174349.
Indices of 12'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..1000] | NthPrime(n+1) - NthPrime(n) eq 12]; // Vincenzo Librandi, Mar 21 2019
  • Mathematica
    Select[Range[1000], Prime[#] + 12 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 21 2019 *)
  • PARI
    A320704_vec(N=100,g=12,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(A031930(n)).
A320704 = { i > 0 | prime(i+1) = prime(i) + 12 }.

A320705 Indices of primes followed by a gap (distance to next larger prime) of 14.

Original entry on oeis.org

30, 62, 66, 137, 146, 150, 162, 223, 250, 283, 309, 350, 360, 382, 402, 410, 424, 434, 503, 514, 526, 532, 536, 570, 610, 649, 654, 666, 687, 704, 706, 747, 780, 790, 867, 906, 919, 929, 967, 978, 981, 992, 1011, 1023, 1038, 1042, 1057, 1072, 1133, 1154, 1160, 1177, 1184
Offset: 1

Views

Author

M. F. Hasler, Oct 19 2018

Keywords

Comments

Indices of the primes listed in A031932.

Links

Crossrefs

Equals A000720 o A031932.
Row 7 of A174349.
Indices of 14'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..1500] | NthPrime(n+1) - NthPrime(n) eq 14]; // Vincenzo Librandi, Mar 19 2019
  • Mathematica
    Select[Range[1500], Prime[#] + 14 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 19 2019 *)
Position[Differences[Prime[Range[1200]]],14]//Flatten (* Harvey P. Dale, Nov 28 2024 *)
  • PARI
    A(N=100,g=14,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(A031932(n)).
A320705 = { i > 0 | prime(i+1) = prime(i) + 14 }.

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}).
Showing 1-10 of 20 results. Next

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