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 1-9 of 9 results.

A037065 Smallest prime containing exactly n 6's.

Original entry on oeis.org

2, 61, 661, 6661, 166667, 666667, 16666669, 66666667, 666666667, 6666666661, 66666666667, 1666666666661, 36666666666661, 166666666666667, 3666666666666667, 16666666666666661, 616666666666666661, 666666666666666661, 36666666666666666661, 66666666666666666667
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Comments

Note that a(11) is palindromic.
The last digit of n cannot be 6, therefore a(n) must have at least n+1 digits. It is probable that none among [10^n/9]*60 + {1,3,7,9} is prime in which case a(n) must have n+2 digits. We conjecture that for all n >= 0, a(n) equals [10^(n+1)/9]*60 + b with 1 <= b <= 9 and one of the (first) digits 6 replaced by a digit among {0, 1, 2, 3, 4, 5}. - M. F. Hasler, Feb 22 2016

Links

Crossrefs

Cf. A065589, A037064, A034388, A036507-A036536.
Cf. A037053, A037055, A037057, A037059, A037061, A037063, A037067, A037069, A037071.

Programs

  • Mathematica
    f[n_, b_] := Block[{k = 10^(n + 1), p = Permutations[ Join[ Table[b, {i, 1, n}], {x}]], c = Complement[Table[j, {j, 0, 9}], {b}], q = {}}, Do[q = Append[q, Replace[p, x -> c[[i]], 2]], {i, 1, 9}]; r = Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]; If[r ? Infinity, r, p = Permutations[ Join[ Table[ b, {i, 1, n}], {x, y}]]; q = {}; Do[q = Append[q, Replace[p, {x -> c[[i]], y -> c[[j]]}, 2]], {i, 1, 9}, {j, 1, 9}]; Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]]]; Table[ f[n, 6], {n, 1, 17}]
  • PARI
    A037065(n)={my(p, t=10^(n+1)\9*60); forvec(v=[[-1, n], [-6, -1]], nextprime(p=t+10^(n-v[1])*v[2])-p<10 && return(nextprime(p)))} \\ M. F. Hasler, Feb 22 2016

Formula

a(n) = prime(A037064(n)). - Amiram Eldar, Jul 21 2025

Extensions

More terms from Hans Havermann, Jun 16 2001
More terms and a(0) = 2 from M. F. Hasler, Feb 22 2016

A037070 a(n)-th prime is the smallest prime containing exactly n 9's.

Original entry on oeis.org

1, 8, 46, 303, 5133, 17984, 216816, 1270607, 41146179, 420243162, 2524038155, 36159205628, 343392568900, 1955010428258, 15237833654620, 260219446617109, 2621513397605657, 24619309639366177, 233874804775621799, 684559920583084690, 20920441130654929928, 200085344903558463823
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037071, A034388.
Cf. A037052, A037054, A037056, A037058, A037060, A037062, A037064, A037066, A037068.

Programs

  • Mathematica
    (* see A037071 for f *) PrimePi[ Table[ f[n, 9], {n, 1, 13}]]

Formula

a(n) = A000720(A037071(n)). - Amiram Eldar, Jul 21 2025

Extensions

One more term from Vladeta Jovovic, Jan 10 2002
a(0)=1 prepended by Sean A. Irvine, Dec 06 2020
a(14)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 21 2025

A037054 a(n)-th prime is the smallest prime containing exactly n 1's.

Original entry on oeis.org

1, 6, 5, 187, 1242, 9682, 86538, 733339, 5821735, 56196114, 503193257, 4161915701, 41621368333, 383118399789, 3549047966306, 33056584174792, 309353882119895, 2651938403956789, 27417323062119921, 27417323062119920, 2461813897281353902, 23422580231698331842
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037055, A034388.
Cf. A037052, A037056, A037058, A037060, A037062, A037064, A037066, A037068, A037070.

Programs

  • Mathematica
    (* see A037055 for f *) PrimePi[ Table[ f[n, 1], {n, 1, 13}]]

Formula

a(n) = A000720(A037055(n)). - Amiram Eldar, Jul 20 2025

Extensions

a(0)=1 prepended by Sean A. Irvine, Dec 06 2020
a(14)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 20 2025

A037056 a(n)-th prime is the smallest prime containing exactly n 2's.

Original entry on oeis.org

2, 1, 48, 331, 2490, 94500, 1283805, 1402294, 12238270, 891573671, 975688072, 77612456753, 715763987889, 748327378591, 6944174236934, 580400102242316, 5209104353769836, 5710407472211223, 510579443617388387, 4806424039483242581, 45763276831811185976, 440594267900327752100
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037057, A034388.
Cf. A037052, A037054, A037058, A037060, A037062, A037064, A037066, A037068, A037070.

Programs

  • Mathematica
    (* see A037057 for f *) PrimePi[ Table[ f[n, 2], {n, 1, 13}]]

Formula

a(n) = A000720(A037057(n)). - Amiram Eldar, Jul 20 2025

Extensions

a(0)=2 prepended by Sean A. Irvine, Dec 06 2020
a(14)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 20 2025

A037058 a(n)-th prime is the smallest prime containing exactly n 3's.

Original entry on oeis.org

1, 2, 51, 345, 2602, 27062, 232466, 1935248, 17950160, 155123231, 1022275037, 13076476440, 119921146473, 1100928006234, 9986615648246, 39453679683959, 636484070277727, 8477216022186037, 80079195779613271, 758351887226957873, 7209429409009441899, 68676498683402943115
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037059, A034388.
Cf. A037052, A037054, A037056, A037060, A037062, A037064, A037066, A037068, A037070.

Programs

  • Mathematica
    (* see A037059 for f *) PrimePi[ Table[ f[n, 3], {n, 1, 13}]]

Formula

a(n) = A000720(A037059(n)). - Amiram Eldar, Jul 20 2025

Extensions

Edited and extended by Robert G. Wilson v, Jul 04 2003
a(0)=1 prepended by Sean A. Irvine, Dec 06 2020
a(14)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 20 2025

A037060 a(n)-th prime is the smallest prime containing exactly n 4's.

Original entry on oeis.org

1, 13, 86, 603, 4620, 37299, 1533327, 22568442, 23574105, 210014510, 1893613727, 17241353173, 493582559244, 13474975578701, 71056054875827, 1180956491651370, 10728352138939963, 103710009988272649, 960912626678471376, 1005142876338508545, 50686811139876408310, 288867303325879381560
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037061, A034388.
Cf. A037052, A037054, A037056, A037058, A037062, A037064, A037066, A037068, A037070.

Programs

  • Mathematica
    (* see A037061 for f *) PrimePi[ Table[ f[n, 4], {n, 1, 12}]]

Formula

a(n) = A000720(A037061(n)). - Amiram Eldar, Jul 20 2025

Extensions

a(0)=1 prepended by Sean A. Irvine, Dec 06 2020
a(13)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 20 2025

A037062 a(n)-th prime is the smallest prime containing exactly n 5's.

Original entry on oeis.org

1, 3, 102, 733, 14319, 45741, 1004275, 3313338, 169807396, 259770566, 20255937351, 21366409911, 196256438549, 10949682060338, 16876678891444, 1376534319069676, 13702579963679833, 13947379867469643, 360360819534753751, 3421022095727840569, 93257415087729395138, 113268191247939457737
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037063, A034388.
Cf. A037052, A037054, A037056, A037058, A037060, A037064, A037066, A037068, A037070.

Programs

  • Mathematica
    (* see A037063 for f *) PrimePi[ Table[ f[n, 5], {n, 1, 12}]]

Formula

a(n) = A000720(A037063(n)). - Amiram Eldar, Jul 20 2025

Extensions

a(0)=1 prepended by Sean A. Irvine, Dec 06 2020
a(13)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 20 2025

A037066 a(n)-th prime is the smallest prime containing exactly n 7's.

Original entry on oeis.org

1, 4, 59, 275, 4924, 58623, 506877, 4546755, 30224014, 87818618, 2836649805, 14748299309, 251285857122, 603200604933, 17530836835060, 80446298927642, 2054098188682332, 9577010472498628, 67026825574168206, 1605887402218872982, 16520076587958693329, 156502536697199220470
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037067, A034388.
Cf. A037052, A037054, A037056, A037058, A037060, A037062, A037064, A037068, A037070.

Programs

  • Mathematica
    (* see A037067 for f *) PrimePi[ Table[ f[n, 7], {n, 1, 12}]]

Formula

a(n) = A000720(A037067(n)). - Amiram Eldar, Jul 21 2025

Extensions

a(0)=1 prepended by Sean A. Irvine, Dec 06 2020
a(14)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 21 2025

A037068 a(n)-th prime is the smallest prime containing exactly n 8's.

Original entry on oeis.org

1, 23, 152, 1107, 8611, 70478, 1793210, 5156463, 45470645, 2074530409, 11397691034, 33578243459, 1603686087003, 2859644709998, 26622184513952, 518238694402971, 2339285051888769, 69641948074252447, 208626752630607267, 8383527978057824838, 119921750787289924042, 375732914981870085595
Offset: 0

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037069, A034388.
Cf. A037052, A037054, A037056, A037058, A037060, A037062, A037064, A037066, A037070.

Programs

  • Mathematica
    (* see A037069 for f *) PrimePi[ Table[ f[n, 8], {n, 1, 13}]]

Formula

a(n) = A000720(A037069(n)). - Amiram Eldar, Jul 21 2025

Extensions

a(0)=1 prepended by Sean A. Irvine, Dec 06 2020
a(12) corrected and a(13)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 21 2025
Showing 1-9 of 9 results.

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