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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A198777 Primes from merging of 3 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

577, 431, 421, 593, 359, 593, 359, 677, 677, 467, 709, 947, 467, 463, 631, 809, 401, 283, 241, 173, 739, 997, 449, 353, 3, 337, 293, 937, 373, 733, 337, 773, 673, 739, 709, 491, 853, 233, 331, 151, 661, 211, 199, 79, 479, 937, 857, 2, 29, 547, 29, 43, 421
Offset: 1

Views

Author

Harvey P. Dale, Oct 29 2011

Keywords

Comments

Leading zeros are permitted, so some terms are less than 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, A104937, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198170, A198171, A198172, A198173, A198175, A104851, A198177, A198776, 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[3]

A104944 Primes from merging of 10 successive digits in decimal expansion of the Euler-Mascheroni constant.

Original entry on oeis.org

7215664901, 1566490153, 3286060651, 6060651209, 9008240243, 4310421593, 2159335939, 9235988057, 8486772677, 8070824809, 2836224173, 3622417399, 3997644923, 2582470949, 6008735203, 3151776611, 5015079847, 7400299213, 3139925401, 3754139549, 7984234877
Offset: 1

Views

Author

Andrew G. West (WestA(AT)wlu.edu), Mar 29 2005

Keywords

Comments

Leading zeros are not permitted, so each term is 10 digits in length. - Harvey P. Dale, Oct 30 2011
See A198784 for the variant without this restriction.-- The original version read (1566490153, 1290642131, 1386514643, 1851726733, 1383679133, 1706757499, 1072945781, 1015442651, 1403043203, 1100525291, 1332985747, 1866475913, 1834810931, 1887149587, 1197399197, 1956311131, 1449885007, 2137384231, ...). These terms are obtained when using signed 32-bit integers, i.e., take the 10-digit strings modulo 2^32, and select the primes between 10^9 and 2^31. - M. F. Hasler, Nov 01 2014

Links

Crossrefs

Cf. A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784.
See also, for e: A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851; for Pi: A104824, A104825, A104826, A198170, A198171, A198172, A198173, A198175; for sqrt(2): A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169; for the golden ratio phi = (sqrt(5)-1)/2: A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A198177.

Programs

  • Mathematica
    egp[len_]:=Module[{egterms=FromDigits/@Partition[RealDigits[EulerGamma, 10, 1000][[1]],len,1]},Select[egterms,IntegerLength[#]==len&&PrimeQ[#]&]];egp[10] (* Harvey P. Dale, Oct 30 2011 *)
  • PARI
    list_A104944(x=Euler, 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 and extended by Harvey P. Dale, Oct 30 2011

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
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