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.

Previous Showing 11-19 of 19 results.

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[#]&]]

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

A105383 Primes between 10^9 and 2^31 obtained from merging 10 successive digits in the decimal expansion of zeta(2) = Pi^2/6, taken modulo 2^32.

Original entry on oeis.org

1902619757, 1896233719, 2025479923, 1979084773, 1834487573, 2069040007, 1357689757, 1422433483, 1421193281, 1865610371, 1664088953, 1716574481, 1524418627, 2018846497, 2028620161, 1384352219, 1828868887, 1485949159
Offset: 1

Views

Author

Andrew G. West (WestA(AT)wlu.edu), Apr 03 2005

Keywords

Comments

Erroneous version of A225143.
The author must have used signed 32-bit integers to store 10 successive digits of zeta(2). This is the sequence you get by taking the 10-digit numbers modulo 2^32 and then listing primes between 10^9 and 2^31 = 2147483648. - Jens Kruse Andersen, Sep 15 2014
In other words, primes p in (10^9, 2^31) such that either p, p + 2^32 or p + 2^32*2 is the concatenation of 10 successive digits in the decimal expansion of Pi^2/6. - Jianing Song, Mar 14 2021

Examples

			From _Jianing Song_, Mar 14 2021: (Start)
1902619757 is a term since 1902619757 + 2^32 = 6197587053 is the concatenation of A013661(92) to A013661(101).
1896233719 is a term since it is the concatenation of A013661(108) to A013661(117). (End)

Links

Crossrefs

Cf. A013661 (decimal expansion of Pi^2/6).
Cf. A103752 (a similar erroneous version).
Cf. (for Pi) A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174 and A104830 (a variant).
Cf. (for e) A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851.
Cf. (for sqrt(2)) A198162, A198163, A198164, A198165, A198166, A198167, A198168,A198169, A198161.
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

  • PARI
    A105383(n, x=Pi^2/6, m=10, silent=0)={m=10^m; for(k=1, default(realprecision), (isprime(p=x\.1^k%m%2^32)&&p*10>m&&p<2^31)||next; silent||print1(p", "); n--||return(p))} \\  Use e.g. \p999 to set precision to 999 digits. - M. F. Hasler, Nov 01 2014

Extensions

Definition updated by M. F. Hasler, Nov 01 2014

A225036 Primes from merging of 10 successive digits in the decimal expansion of Pi^2.

Original entry on oeis.org

5913774023, 9137740231, 7402314407, 4023144077, 8735261779, 4830981887, 8309818873, 3307626667, 8853659527, 6595276357, 5952763577, 7635775283, 3577528379, 3792268331, 9085975607, 9264752779, 6698082641, 8968771057, 1057327889, 5972589229, 4137067777
Offset: 1

Views

Author

Bruno Berselli, Apr 25 2013

Keywords

Comments

Leading zeros are not permitted, so each prime is 10 digits in length. The terms are listed in the order in which they occur.

Links

Crossrefs

Cf. A002388, A104925 - A104932, A198174.
Cf. A104933.

Programs

  • Mathematica
    With[{len = 10}, FromDigits /@ Select[Partition[RealDigits[Pi^2, 10, 600][[1]], len, 1], PrimeQ[FromDigits[#]] && IntegerLength[FromDigits[#]] == len &]]
Previous Showing 11-19 of 19 results.

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