A104830 -id:A104830 - cp's OEIS frontend

A198174 Primes from merging of 10 successive digits in decimal expansion of Pi, in the order of appearance.

5926535897, 4197169399, 1693993751, 7510582097, 4825342117, 5822317253, 2841027019, 8521105559, 8954930381, 4756482337, 2712019091, 5432664821, 3266482133, 6072602491, 5588174881, 8815209209, 6282925409, 2540917153, 5903600113, 8204665213, 3841469519

Offset: 1

Harvey P. Dale, Oct 21 2011

Leading zeros are not permitted, so each term is 10 digits in length.

See A104830 for the variant without this restriction. - M. F. Hasler, Nov 01 2014

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

Cf., for Pi: A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174 (this) and A104830 (a variant).
Cf., for sqrt(2): A198162, A198163, A198164, A198165,A198166, A198167, A198168, A198169, A198161.
Cf., for e: A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851.
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.

With[{len=10},Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]], len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198174(n, x=Pi, m=10, silent=0)={m=10^m; for(k=1, default(realprecision), (isprime(p=x\.1^k%m)&&p*10>m)||next; silent||print1(p", "); n--||return(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

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

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A198174 Primes from merging of 10 successive digits in decimal expansion of Pi, in the order of appearance.

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