|
%I #32 Feb 10 2024 16:44:01
%S 1902619757,1896233719,2025479923,1979084773,1834487573,2069040007,
%T 1357689757,1422433483,1421193281,1865610371,1664088953,1716574481,
%U 1524418627,2018846497,2028620161,1384352219,1828868887,1485949159
%N 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.
%C Erroneous version of A225143.
%C 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
%C 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
%H Simon Plouffe, <a href="https://web.archive.org/web/20080205213252/http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap96.html">10000 digits of Zeta(2)</a>.
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.
%e From _Jianing Song_, Mar 14 2021: (Start)
%e 1902619757 is a term since 1902619757 + 2^32 = 6197587053 is the concatenation of A013661(92) to A013661(101).
%e 1896233719 is a term since it is the concatenation of A013661(108) to A013661(117). (End)
%o (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
%Y Cf. A013661 (decimal expansion of Pi^2/6).
%Y Cf. A103752 (a similar erroneous version).
%Y Cf. (for Pi) A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174 and A104830 (a variant).
%Y Cf. (for e) A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851.
%Y Cf. (for sqrt(2)) A198162, A198163, A198164, A198165, A198166, A198167, A198168,A198169, A198161.
%Y Cf. (for the Golden Ratio) A198177, A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812.
%Y Cf., for the Euler-Mascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784.
%K nonn,base
%O 1,1
%A Andrew G. West (WestA(AT)wlu.edu), Apr 03 2005
%E Definition updated by _M. F. Hasler_, Nov 01 2014
|
