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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A198167 Primes from merging of 7 successive digits in decimal expansion of sqrt(2).

Original entry on oeis.org

3562373, 5048801, 2420969, 5038753, 7534327, 6415727, 5073721, 2126441, 2644121, 9709993, 9935831, 2226659, 9275579, 8206057, 5714701, 7027453, 2851741, 8640889, 2145083, 5835239, 3868999, 8689997, 9970699, 9900481, 2779031, 6311159, 6668713, 6871301
Offset: 1

Views

Author

Harvey P. Dale, Oct 21 2011

Keywords

Comments

Leading zeros are not permitted, so each term is 7 digits in length.

Links

Crossrefs

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198168, A198169, A198170, A198171, A198172, A198173, A198174, A198175, A104851, A198177.

Programs

  • Mathematica
    With[{len=7},Select[FromDigits/@Partition[RealDigits[Sqrt[2],10,1000][[1]],len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198168 Primes from merging of 8 successive digits in decimal expansion of sqrt(2).

Original entry on oeis.org

42135623, 98078569, 96718753, 76948073, 69480731, 31766797, 76679737, 24784621, 70388503, 64157273, 22970249, 35831413, 75055927, 82060571, 71470109, 55232923, 21450839, 25835239, 23950547, 57502877, 87759961, 18570113, 54374603, 16038689, 38689997, 99970699
Offset: 1

Views

Author

Harvey P. Dale, Oct 21 2011

Keywords

Comments

Leading zeros are not permitted, so each term is 8 digits in length.

Links

Crossrefs

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198169, A198170, A198171, A198172, A198173, A198174, A198175, A104851, A198177

Programs

  • Mathematica
    With[{len=8},Select[FromDigits/@Partition[RealDigits[Sqrt[2],10,1000][[1]],len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198170 Primes from merging of 3 successive digits in decimal expansion of Pi.

Original entry on oeis.org

653, 643, 433, 383, 419, 197, 971, 937, 751, 307, 421, 211, 821, 823, 647, 709, 223, 317, 359, 811, 701, 193, 521, 211, 229, 881, 109, 659, 593, 461, 823, 233, 337, 271, 821, 607, 491, 127, 587, 631, 881, 881, 829, 409, 643, 367, 113, 521, 941, 151, 433, 727
Offset: 1

Views

Author

Harvey P. Dale, Oct 21 2011

Keywords

Comments

Leading zeros are not permitted, so each term is 3 digits in length.

Links

Crossrefs

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198171, A198172, A198173, A198174, A198175, A104851, A198177.

Programs

  • Mathematica
    Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]],3,1], IntegerLength[#]==3&&PrimeQ[#]&]

A198171 Primes from merging of 7 successive digits in decimal expansion of Pi forbidding leading zeros.

Original entry on oeis.org

1592653, 6535897, 2643383, 5028841, 6939937, 3993751, 1170679, 8086513, 5822317, 1725359, 4930381, 2881097, 4612847, 3165271, 2712019, 1201909, 4914127, 1133053, 3841469, 1469519, 6951941, 9433057, 9326117, 4462379, 2749567, 5272489, 8912279, 8183011
Offset: 1

Views

Author

Harvey P. Dale, Oct 21 2011

Keywords

Comments

Leading zeros are not permitted, so each term is 7 digits in length.

Links

Crossrefs

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198170, A198172, A198173, A198174, A198175, A104851, A198177.

Programs

  • Mathematica
    With[{len=7},Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]], len,1], IntegerLength[#]==len&&PrimeQ[#]&]]

A198172 Primes from merging of 8 successive digits in decimal expansion of Pi forbidding leading zeros.

Original entry on oeis.org

28841971, 41971693, 82534211, 42117067, 30664709, 31725359, 49303819, 75648233, 37867831, 71201909, 48566923, 26648213, 13393607, 25409171, 57595919, 21861173, 81932611, 79962749, 24891227, 30119491, 40656643, 30860213, 39494639, 39522473, 98609437, 53921717
Offset: 1

Views

Author

Harvey P. Dale, Oct 21 2011

Keywords

Comments

Leading zeros are not permitted, so each term is 8 digits in length.

Links

Crossrefs

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198170, A198171, A198173, A198174, A198175, A104851, A198177.

Programs

  • Mathematica
    With[{len=8},Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]], len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198173 Primes from merging of 9 successive digits in decimal expansion of Pi forbidding leading zeros.

Original entry on oeis.org

795028841, 502884197, 884197169, 971693993, 348253421, 421170679, 306647093, 812848111, 659334461, 233786783, 648566923, 346034861, 326648213, 829254091, 678925903, 959195309, 530921861, 938183011, 298336733, 798609437, 717629317, 320005681, 757789609
Offset: 1

Views

Author

Harvey P. Dale, Oct 21 2011

Keywords

Comments

Leading zeros are not permitted, so each term is 9 digits in length.

Links

Crossrefs

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198170, A198171, A198172, A198174, A198175, A104851, A198177.

Programs

  • Mathematica
    With[{len=9},Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]], len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198175 Primes from merging of 2 successive digits in decimal expansion of Pi.

Original entry on oeis.org

31, 41, 59, 53, 89, 97, 79, 23, 43, 83, 79, 41, 19, 97, 71, 37, 97, 59, 23, 89, 53, 11, 17, 67, 79, 13, 23, 47, 23, 31, 17, 53, 59, 11, 11, 17, 41, 19, 11, 59, 29, 89, 19, 97, 59, 61, 47, 23, 37, 67, 83, 31, 71, 19, 23, 61, 43, 13, 41, 73, 37, 31, 17, 29, 17
Offset: 1

Views

Author

Harvey P. Dale, Oct 21 2011

Keywords

Comments

Leading zeros are not permitted, so each term is 2 digits in length.

Links

Crossrefs

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198170, A198171, A198172, A198173, A198174, A104851, A198177.

Programs

  • Mathematica
    With[{len=2},Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]], len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198174 Primes from merging of 10 successive digits in decimal expansion of Pi, in the order of appearance.

Original entry on oeis.org

5926535897, 4197169399, 1693993751, 7510582097, 4825342117, 5822317253, 2841027019, 8521105559, 8954930381, 4756482337, 2712019091, 5432664821, 3266482133, 6072602491, 5588174881, 8815209209, 6282925409, 2540917153, 5903600113, 8204665213, 3841469519
Offset: 1

Views

Author

Harvey P. Dale, Oct 21 2011

Keywords

Comments

Leading zeros are not permitted, so each term is 10 digits in length.
See A104830 for the variant without this restriction. - M. F. Hasler, Nov 01 2014

Links

Crossrefs

Cf., for Pi: A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174 (this) and A104830 (a variant).
Cf., for sqrt(2): A198162, A198163, A198164, A198165,A198166, A198167, A198168, A198169, A198161.
Cf., for e: A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851.
Cf., for the Golden Ratio: A198177, A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812.
Cf., for the Euler-Mascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784.

Programs

  • Mathematica
    With[{len=10},Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]], len,1],IntegerLength[#]==len&&PrimeQ[#]&]]
  • PARI
    A198174(n, x=Pi, m=10, silent=0)={m=10^m; for(k=1, default(realprecision), (isprime(p=x\.1^k%m)&&p*10>m)||next; silent||print1(p", "); n--||return(p))} \\ The optional arguments can be used to produce other sequences of this series (cf. Crossrefs). Use e.g. \p999 to set precision to 999 digits. - M. F. Hasler, Nov 01 2014

A198776 Primes from merging of 2 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

53, 2, 43, 31, 59, 59, 23, 59, 5, 67, 23, 67, 67, 67, 47, 29, 17, 67, 31, 47, 7, 5, 83, 41, 17, 73, 97, 23, 53, 53, 3, 37, 29, 37, 73, 37, 73, 37, 67, 73, 79, 59, 47, 73, 3, 67, 53, 23, 31, 17, 61, 11, 11, 19, 7, 79, 47, 79, 37, 5, 2, 29, 13, 47, 61, 2, 29
Offset: 1

Views

Author

Harvey P. Dale, Oct 29 2011

Keywords

Comments

Leading zeros are permitted, so some terms may be less than 2 digits in length.

Links

Crossrefs

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811,
A103812, A104824, A104825, A104826, A104843, A104844, A104845,
A104846, A104847, A104848, A104849, A104850, A104936, A198161, A198162,
A198163, A198164, A198165, A198166, A198167, A198168, A198169,
A198170, A198171, A198172, A198173, A198175, A104851, A198177,
A198777, A198778, A198779, A198780, A198781, A198782,
A198783, A198784.

Programs

  • Mathematica
      egp[len_]:=Module[{egterms=FromDigits/@Partition[RealDigits[EulerGamma, 10, 1000][[1]],len,1]},Select[egterms,PrimeQ[#]&]];egp[2]
Select[FromDigits/@Partition[RealDigits[EulerGamma,10,500][[1]],2,1],PrimeQ] (* Harvey P. Dale, Mar 19 2020 *)

A198784 Primes from merging of 10 successive digits in decimal expansion of Euler-Mascheroni constant (in the order of appearance).

Original entry on oeis.org

7215664901, 1566490153, 3286060651, 6060651209, 9008240243, 4310421593, 2159335939, 9235988057, 8486772677, 8070824809, 2836224173, 3622417399, 3997644923, 33374293, 2582470949, 6008735203, 87352039, 3151776611, 5015079847, 7400299213, 3139925401, 3754139549
Offset: 1

Views

Author

Harvey P. Dale, Oct 29 2011

Keywords

Comments

Leading zeros are permitted, so some terms are less than 10 digits in length.
See A104944 for the variant where no leading zeros are allowed. - M. F. Hasler, Nov 01 2014

Links

Crossrefs

For the Euler-Mascheroni constant, see also A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784 (this sequence) and A104944 (a variant).
For sqrt(2), see A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198161.
For e, see A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851.
For Pi, see A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174.
For the Golden Ratio, see A198177, A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812.

Programs

  • Mathematica
    egp[len_]:=Module[{egterms=FromDigits/@Partition[RealDigits[EulerGamma, 10, 1000][[1]],len,1]},Select[egterms,PrimeQ[#]&]]; egp[10]
  • PARI
    list_A198784(x=Euler,m=10)=m=10^m;for(k=1,default(realprecision),isprime(p=x\.1^k%m)&&print1(p",")) \\ The optional arguments can be used to produce other sequences of this series (cf. Crossrefs). Use e.g. \p999 to set precision to 999 digits. - M. F. Hasler, Nov 01 2014
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