A104847 -id:A104847 - cp's OEIS frontend

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

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

Harvey P. Dale, Oct 29 2011

Leading zeros are permitted, so some terms are less than 3 digits in length.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

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

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

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Jon Borwein, 170,000 digits of Gamma [Wayback Machine copy]
Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant.

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.

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 *)

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

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

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

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

			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)

Simon Plouffe, 10000 digits of Zeta(2).
Eric Weisstein, Riemann Zeta Function.

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.

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

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

A120625 Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 3n.

Original entry on oeis.org

15, 20, 42, 77, 88, 104, 126, 140, 153, 156, 170, 187, 190, 204, 209, 210, 220, 228, 231, 238, 240, 266, 299, 308, 312, 322, 368, 420, 429, 435, 440, 442, 450, 460, 464, 468, 476, 483, 493, 496, 510, 527, 551, 558, 561, 580, 589, 600, 609, 620, 624, 651, 665

Offset: 1

Robert G. Wilson v, Jun 19 2006

nonn

Equivalently, numbers n such that the n-th central binomial coefficient C(2n,n) is divisible by 3n(n+1). - Joel B. Lewis, Jan 07 2008

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Subset of A104847, Cf. A120623.

fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(3n(n + 1))]; Select[ Range@681, fQ@# &]
With[{nn=700},Transpose[Select[Thread[{CatalanNumber[Range[nn]],Range[ nn]}],Divisible[#[[1]],3#[[2]]]&]][[2]]] (* Harvey P. Dale, Apr 30 2012 *)

Definition corrected by Joel B. Lewis, Apr 30 2009

cp's OEIS Frontend

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

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

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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.

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Crossrefs

Programs

PARI

Extensions

A120625 Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 3n.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions