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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A104851 Primes from merging of 10 successive digits in decimal expansion of e.

Original entry on oeis.org

7427466391, 7413596629, 6059563073, 3490763233, 2988075319, 1573834187, 7021540891, 5408914993, 6480016847, 9920695517, 1838606261, 6062613313, 3845830007, 1692836819, 4425056953, 2505695369, 5490598793, 1782154249, 8215424999, 9229576351, 9519366803
Offset: 1

Views

Author

Andrew G. West (WestA(AT)wlu.edu), Mar 27 2005

Keywords

Comments

Scan decimal expansion of e from left to right, recording any 10-digit primes seen. - N. J. A. Sloane, Feb 05 2012
All the primes listed here must have 10 digits, i.e., "leading zeros are not allowed". Otherwise, one would also have some terms as 297606737 or 865746377 or 98793127 from A104850. - M. F. Hasler, Nov 01 2014
The original version read (1185790117, 1180978417, 1573834187, 1838606261, 1308008771, 1692836819, 1782154249, 1825288693, 1525971943, 1730123819, 1332069811, 1881593041, 1934580727, 1978623209, 1164218399, 1574862173, 1635834619, 1311914371, ...). These terms are obtained when using signed 32-bit integers, i.e., take the 10-digit numbers modulo 2^32, and select the primes between 10^9 and 2^31. - M. F. Hasler, Nov 01 2014

Links

Crossrefs

For e, see also A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851 (this).
For Pi, see A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174.
For sqrt(2), see A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198161.
For the Golden Ratio, see A198177, A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812; A103752.
For the Euler-Mascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784.

Programs

  • Mathematica
    With[{de=FromDigits/@Partition[RealDigits[E,10,10000][[1]],10,1]}, Select[de,#>10^9&&PrimeQ[#]&]] (* Harvey P. Dale, Feb 05 2012 *)
  • PARI
    list_A104851(x=exp(1), m=10)=m=10^m; for(k=1, default(realprecision), isprime(p=x\.1^k%m)&&p*10>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

Extensions

Corrected by Harvey P. Dale, Feb 05 2012
Offset changed from 0 to 1 by Vincenzo Librandi, Apr 21 2013

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 *)
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