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

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

Offset: 1

Author

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

Keywords

• nonn
• base

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

• 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.

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