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.

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..18.

Simon Plouffe, 10000 digits of Zeta(2).

Eric Weisstein, Riemann Zeta Function.

Example

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)

Prog

(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

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.

Sequence in context: A263562 A204813 A103752 * A339251 A233002 A165075

Adjacent sequences: A105380 A105381 A105382 * A105384 A105385 A105386

Keyword

nonn,base

Author

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

Extensions

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

Status

approved