A198177 -id:A198177 - cp's OEIS frontend

A198778 Primes from merging of 4 successive digits in decimal expansion of Euler-Mascheroni constant A001620.

577, 421, 3359, 3593, 5939, 9923, 8677, 2677, 6709, 6947, 6329, 2917, 4951, 1447, 401, 4283, 2417, 6449, 5003, 3733, 3767, 7673, 9491, 2039, 853, 5323, 6211, 4793, 7937, 857, 7057, 29, 3547, 6043, 587, 6733, 7331, 3313, 1399, 7541, 5413, 4139, 8423, 4877, 503, 8431, 3109, 1093, 9973, 3613, 8893, 8933, 17, 7247

Offset: 1

Harvey P. Dale, Oct 29 2011

In contrast to A104938, leading zeros are allowed here, which explains the terms having fewer than 4 digits; e.g., a(32)=29 comes from consecutive digits "...0029..." starting at the 268th decimal digit of gamma (if the initial "0." counts as the first digit). - M. F. Hasler, Oct 31 2011

			The first four decimal digits of gamma = 0.5772... form the prime 577=a(1).

Cf. A103773, A103789, A103793, A103808-A103812, A104824-A104826, A104843-A104850, A198161-A198177, A198776-A198784.

Digits := 420 ;
for sh from 3 do
        p := floor(gamma*10^sh) mod 10000 ;
        if isprime(p) then
                printf("%d,",p);
        end if;
end do: # R. J. Mathar, Oct 31 2011

(* see A104938 for Mmca code *)
Join[{577},Select[FromDigits/@Partition[RealDigits[EulerGamma,10,1000][[1]],4,1],PrimeQ]] (* Harvey P. Dale, May 07 2019 *)

L=10^4;for(i=3,999,isprime(p=Euler\.1^i%L)&print1(p",")) \\ M. F. Hasler, Oct 31 2011

A198779 Primes from merging of 5 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

64901, 59399, 48677, 77267, 26777, 66467, 36947, 6329, 32917, 17467, 49807, 24809, 92353, 50033, 74293, 42937, 37337, 33773, 79259, 24709, 70949, 9491, 16567, 70853, 53233, 33151, 31517, 28621, 62119, 79847, 98479, 84793, 50857, 29921, 14669, 96043, 35267, 52673, 40129, 12967

Offset: 1

Harvey P. Dale, Oct 29 2011

In contrast to A104939, leading zeros are permitted, so this sequence contains all elements of A104939 and additional primes having fewer than 5 digits.

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

Cf. A186206, A103773, A103789, A103793, A103808-A103812, A104824-A104826, A104843-A104850, A198161-A198177, A198776-A198784.

egp[len_] := Module[{egterms = FromDigits /@ Partition[RealDigits[EulerGamma, 10, 400][[1]], len, 1]}, Select[egterms, PrimeQ[#] &]]; egp[5] (* Vincenzo Librandi, Apr 20 2013 *)

A198780 Primes from merging of 6 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

939923, 992359, 746749, 241739, 644923, 350033, 500333, 374293, 937337, 773767, 160087, 670853, 532331, 199501, 79847, 847937, 29921, 299213, 325421, 526733, 673313, 331399, 12967, 375413, 395491, 954911, 38431, 93997, 939973, 60889, 271351, 349291, 79843, 984301, 341777

Offset: 1

Harvey P. Dale, Oct 29 2011

In contrast to A104940, leading zeros are permitted, so this sequence contains all terms of A104940 plus additional primes with fewer than 6 digits.

Cf. A186206, A103773, A103789, A103793, A103808-A103812, A104824-A104826, A104843-A104850, A198161-A198177, A198776-A198784.

A198781 Primes from merging of 7 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

2402431, 5933593, 8677267, 7726777, 6467093, 6709369, 6947063, 2417399, 7394279, 4709491, 9160087, 5670853, 8532331, 1528621, 7984793, 7400299, 29921, 299213, 2542151, 5190587, 3754139, 1395491, 1116851, 4234877, 1093997, 939973, 3997361, 6088933, 2676001, 7247953

Offset: 1

Harvey P. Dale, Oct 29 2011

In contrast to A104941, leading zeros are permitted, so this sequence contains all terms of A104941 plus additional primes with fewer than 7 digits.

Cf. A186206, A103773, A103789, A103793, A103808-A103812, A104824-A104826, A104843-A104850, A198161-A198177, A198776-A198784.

A198782 Primes from merging of 8 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

72156649, 31042159, 35939923, 93992359, 98805767, 80576723, 77766467, 36947063, 33374293, 33742937, 42937337, 33773767, 25824709, 87352039, 8532331, 15286211, 28621199, 50798479, 7984793, 299213, 40296043, 51028079, 80798423, 84234877, 20503843, 93997361, 6088933

Offset: 1

Harvey P. Dale, Oct 29 2011

In contrast to A104942, leading zeros are permitted, so this sequence contains all terms of A104942 and additional primes with fewer than 8 digits.

Cf. A103773, A103789, A103793, A103808-A103812, A104824-A104826, A104843-A104850, A198161-A198177, A198776-A198784.

A198783 Primes from merging of 9 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

215664901, 593359399, 235988057, 362241739, 739976449, 33374293, 337429373, 733773767, 87352039, 670853233, 146694029, 151905877, 267331399, 413954911, 984234877, 384310939, 310939973, 93997361, 939973613, 306088933, 60889331, 759271351, 549570661, 789358679

Offset: 1

Harvey P. Dale, Oct 29 2011

In contrast to A104943, leading zeros are permitted, so this sequence contains all terms of A104943 and additional primes with fewer than 9 digits.

Cf. A103773, A103789, A103793, A103808-A103812, A104824-A104826, A104843-A104850, A198161-A198177, A198776-A198784.

Digits := 620 ;
for sh from 8 do
        p := floor(gamma*10^sh) mod 1000000000 ;
        if isprime(p) then
                printf("%d,",p);
        end if;
end do: # R. J. Mathar, Oct 31 2011

Select[FromDigits/@Partition[RealDigits[EulerGamma,10,520][[1]],9,1],PrimeQ] (* Harvey P. Dale, Jun 03 2021 *)

A103752 Erroneous version of: Primes from merging of 10 successive digits in decimal expansion of the Golden Ratio: (1+sqrt(5))/2.

Original entry on oeis.org

1885371871, 1467894749, 1927385857, 1044320141, 1696498873, 1208796539, 1404814871, 1388362561, 1165339067, 1653392113, 1112115161, 1678526879, 1021710497, 1225884823, 1092051469, 2035361123, 1439829827, 1122708877

Offset: 0

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

What is this sequence? The correct version is A198177. - Bruno Berselli, May 01 2013

All terms are less than 2^31, this seems to indicate that the author made calculations with signed 32-bit integers, similar to A105383. But in contrast to that sequence, none of the terms here is obtained by using this procedure (taking mod 2^32 and selecting primes between 10^9 and 2^31). Does the present sequence rather relate to a different constant? - M. F. Hasler, Nov 01 2014

Simon Plouffe, Expansion of the Golden Ratio done to 20,000 digits as part of project Gutenberg.
Eric Weisstein's World of Mathematics, Golden Ratio.

Cf. A198177.

Broken URL to Project Gutenberg replaced by Georg Fischer, Jan 03 2009

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

A104938 Primes from merging of 4 successive digits in decimal expansion of the Euler-Mascheroni constant A001620.

Original entry on oeis.org

3359, 3593, 5939, 9923, 8677, 2677, 6709, 6947, 6329, 2917, 4951, 1447, 4283, 2417, 6449, 5003, 3733, 3767, 7673, 9491, 2039, 5323, 6211, 4793, 7937, 7057, 3547, 6043, 6733, 7331, 3313, 1399, 7541, 5413, 4139, 8423, 4877, 8431, 3109, 1093, 9973, 3613

Offset: 1

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

Leading zeros are not permitted, so each term is 4 digits in length.

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. A198778.

Cf. A103773, A103789, A103793, A103808 - A103812, A104824- A104826, A104843 - A104850, A198161 - A198177, A198776 - A198784. - Harvey P. Dale, Oct 29 2011

Digits := 420 ;
for sh from 3 do
        p := floor(gamma*10^sh) mod 10000 ;
        if isprime(p) and p > 999 then
                printf("%d,",p);
        end if;
end do: # R. J. Mathar, Oct 31 2011

egp[len_]:=Module[{egterms=FromDigits/@Partition[RealDigits[EulerGamma, 10, 1000][[1]],len,1]},Select[egterms,IntegerLength[#]==len&&PrimeQ[#]&]]; egp[4] (* Harvey P. Dale, Oct 29 2011 *)

L=10^4;for(i=3,999,isprime(p=Euler\.1^i%L)&p*10>L&print1(p",")) \\ M. F. Hasler, Oct 31 2011

Offset changed from 0 to 1 by Vincenzo Librandi, Apr 21 2013

cp's OEIS Frontend

A198778 Primes from merging of 4 successive digits in decimal expansion of Euler-Mascheroni constant A001620.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica

PARI

A198779 Primes from merging of 5 successive digits in decimal expansion of Euler-Mascheroni constant.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A198780 Primes from merging of 6 successive digits in decimal expansion of Euler-Mascheroni constant.

Views

Author

Keywords

Comments

Crossrefs

A198781 Primes from merging of 7 successive digits in decimal expansion of Euler-Mascheroni constant.

Views

Author

Keywords

Comments

Crossrefs

A198782 Primes from merging of 8 successive digits in decimal expansion of Euler-Mascheroni constant.

Views

Author

Keywords

Comments

Crossrefs

A198783 Primes from merging of 9 successive digits in decimal expansion of Euler-Mascheroni constant.

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

A103752 Erroneous version of: Primes from merging of 10 successive digits in decimal expansion of the Golden Ratio: (1+sqrt(5))/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions

A104938 Primes from merging of 4 successive digits in decimal expansion of the Euler-Mascheroni constant A001620.

Views