A104843 -id:A104843 - cp's OEIS frontend

A198165 Primes from merging of 5 successive digits in decimal expansion of sqrt(2).

56237, 37309, 78569, 67187, 48073, 76679, 66797, 97379, 79907, 50387, 34327, 64157, 15727, 91229, 70249, 73721, 12149, 70999, 35831, 65927, 55927, 55799, 11527, 55997, 59971, 86201, 20147, 28517, 88919, 30871, 14321, 45083, 50839, 62603, 51407, 87253, 72533

Offset: 1

Harvey P. Dale, Oct 21 2011

Leading zeros are not permitted, so each term is 5 digits in length.

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

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198166, A198167, A198168, A198169, A198170, A198171, A198172, A198173, A198174, A198175, A104851, A198177.

With[{len=5},Select[FromDigits/@Partition[RealDigits[Sqrt[2],10,1000][[1]], len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198166 Primes from merging of 6 successive digits in decimal expansion of sqrt(2).

Original entry on oeis.org

135623, 569671, 480731, 850387, 157273, 384623, 585073, 970999, 927557, 275579, 950501, 686201, 450839, 514079, 989687, 872533, 583523, 750287, 759961, 961729, 983557, 752203, 531857, 857011, 570113, 374603, 340849, 868999, 997069, 970699, 900481, 277903

Offset: 1

Harvey P. Dale, Oct 21 2011

Leading zeros are not permitted, so each term is 6 digits in length.

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

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198167, A198168, A198169, A198170, A198171, A198172, A198173, A198174, A198175, A104851, A198177.

With[{len=6},Select[FromDigits/@Partition[RealDigits[Sqrt[2],10,1000][[1]], len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A104845 Primes from merging of 4 successive digits in decimal expansion of e.

Original entry on oeis.org

4523, 8747, 7757, 7247, 5749, 6967, 6277, 3547, 4759, 3821, 6427, 4663, 3919, 2003, 1741, 9043, 4357, 8627, 4349, 6323, 8807, 5101, 1019, 1901, 9011, 1879, 1499, 4993, 2447, 7741, 7411, 8537, 4243, 2437, 3907, 2069, 9551, 7027, 6133, 3313, 4583, 4493

Offset: 1

Andrew G. West (WestA(AT)wlu.edu), Mar 27 2005

Leading zeros are not permitted, so each term is 4 digits in length. - Harvey P. Dale, Oct 23 2011

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

Cf. A104843-A104862.

With[{len=4},FromDigits/@Select[Partition[RealDigits[E,10,1000][[1]], len,1],PrimeQ[FromDigits[#]]&&IntegerLength[FromDigits[#]]==len&]] (* Harvey P. Dale, Oct 23 2011 *)

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

A104846 Primes from merging of 5 successive digits in decimal expansion of e.

Original entry on oeis.org

74713, 62497, 24977, 24709, 47093, 95957, 49669, 27427, 46639, 32003, 59921, 21817, 35729, 63073, 28627, 27943, 94349, 33829, 98807, 57383, 41879, 18793, 91499, 68477, 47741, 37423, 42437, 24371, 10753, 17027, 61331, 13313, 93287

Offset: 1

Andrew G. West (WestA(AT)wlu.edu), Mar 27 2005

Leading zeros are not permitted, so each term is 5 digits in length. - Harvey P. Dale, Oct 23 2011

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

Cf. A104843-A104862.

With[{len=5},FromDigits/@Select[Partition[RealDigits[E,10,1000][[1]], len,1],PrimeQ[FromDigits[#]]&&IntegerLength[FromDigits[#]]==len&]] (* Harvey P. Dale, Oct 23 2011 *)

Offset changed from 0 to 1 by Vincenzo Librandi, Apr 20 2013

A104848 Primes from merging of 7 successive digits in decimal expansion of e.

Original entry on oeis.org

2718281, 6028747, 2497757, 5354759, 4759457, 7594571, 5945713, 7138217, 3059921, 9921817, 6059563, 6307381, 3073813, 9525101, 5251019, 4089149, 8914993, 9348841, 4167509, 7774499, 8606261, 2613313, 5830007, 1274437

Offset: 1

Andrew G. West (WestA(AT)wlu.edu), Mar 27 2005

Leading zeros are not permitted, so each term is 7 digits in length. - Harvey P. Dale, Oct 23 2011

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

Cf. A104843-A104862.

With[{len=7},FromDigits/@Select[Partition[RealDigits[E,10,1000][[1]], len,1],PrimeQ[FromDigits[#]]&&IntegerLength[FromDigits[#]]==len&]] (* Harvey P. Dale, Oct 23 2011 *)

Offset changed from 0 to 1 by Vincenzo Librandi, Apr 19 2013

A104849 Primes from merging of 8 successive digits in decimal expansion of e.

Original entry on oeis.org

72407663, 40766303, 54759457, 57138217, 20030599, 98807531, 15738341, 83418793, 34884167, 84167509, 22648001, 10753907, 20695517, 38606261, 82656029, 29760673, 13200709, 27443747, 74704723, 69772093, 92836819

Offset: 1

Andrew G. West (WestA(AT)wlu.edu), Mar 27 2005

Leading zeros are not permitted, so each term is 8 digits in length. - Harvey P. Dale, Oct 23 2011

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

Cf. A104843-A104862.

With[{len=8},FromDigits/@Select[Partition[RealDigits[E,10,1000][[1]], len,1],PrimeQ[FromDigits[#]]&&IntegerLength[FromDigits[#]]==len&]] (* Harvey P. Dale, Oct 23 2011 *)

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

A104851 Primes from merging of 10 successive digits in decimal expansion of e.

Original entry on oeis.org

7427466391, 7413596629, 6059563073, 3490763233, 2988075319, 1573834187, 7021540891, 5408914993, 6480016847, 9920695517, 1838606261, 6062613313, 3845830007, 1692836819, 4425056953, 2505695369, 5490598793, 1782154249, 8215424999, 9229576351, 9519366803

Offset: 1

Andrew G. West (WestA(AT)wlu.edu), Mar 27 2005

Scan decimal expansion of e from left to right, recording any 10-digit primes seen. - N. J. A. Sloane, Feb 05 2012
All the primes listed here must have 10 digits, i.e., "leading zeros are not allowed". Otherwise, one would also have some terms as 297606737 or 865746377 or 98793127 from A104850. - M. F. Hasler, Nov 01 2014
The original version read (1185790117, 1180978417, 1573834187, 1838606261, 1308008771, 1692836819, 1782154249, 1825288693, 1525971943, 1730123819, 1332069811, 1881593041, 1934580727, 1978623209, 1164218399, 1574862173, 1635834619, 1311914371, ...). These terms are obtained when using signed 32-bit integers, i.e., take the 10-digit numbers 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

For e, see also A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851 (this).
For Pi, see A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174.
For sqrt(2), see A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198161.
For the Golden Ratio, see A198177, A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812; A103752.
For the Euler-Mascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784.

With[{de=FromDigits/@Partition[RealDigits[E,10,10000][[1]],10,1]}, Select[de,#>10^9&&PrimeQ[#]&]] (* Harvey P. Dale, Feb 05 2012 *)

list_A104851(x=exp(1), 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 by Harvey P. Dale, Feb 05 2012

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

A198167 Primes from merging of 7 successive digits in decimal expansion of sqrt(2).

Original entry on oeis.org

3562373, 5048801, 2420969, 5038753, 7534327, 6415727, 5073721, 2126441, 2644121, 9709993, 9935831, 2226659, 9275579, 8206057, 5714701, 7027453, 2851741, 8640889, 2145083, 5835239, 3868999, 8689997, 9970699, 9900481, 2779031, 6311159, 6668713, 6871301

Offset: 1

Harvey P. Dale, Oct 21 2011

Leading zeros are not permitted, so each term is 7 digits in length.

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

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198168, A198169, A198170, A198171, A198172, A198173, A198174, A198175, A104851, A198177.

With[{len=7},Select[FromDigits/@Partition[RealDigits[Sqrt[2],10,1000][[1]],len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198168 Primes from merging of 8 successive digits in decimal expansion of sqrt(2).

Original entry on oeis.org

42135623, 98078569, 96718753, 76948073, 69480731, 31766797, 76679737, 24784621, 70388503, 64157273, 22970249, 35831413, 75055927, 82060571, 71470109, 55232923, 21450839, 25835239, 23950547, 57502877, 87759961, 18570113, 54374603, 16038689, 38689997, 99970699

Offset: 1

Harvey P. Dale, Oct 21 2011

Leading zeros are not permitted, so each term is 8 digits in length.

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

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198169, A198170, A198171, A198172, A198173, A198174, A198175, A104851, A198177

With[{len=8},Select[FromDigits/@Partition[RealDigits[Sqrt[2],10,1000][[1]],len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198170 Primes from merging of 3 successive digits in decimal expansion of Pi.

Original entry on oeis.org

653, 643, 433, 383, 419, 197, 971, 937, 751, 307, 421, 211, 821, 823, 647, 709, 223, 317, 359, 811, 701, 193, 521, 211, 229, 881, 109, 659, 593, 461, 823, 233, 337, 271, 821, 607, 491, 127, 587, 631, 881, 881, 829, 409, 643, 367, 113, 521, 941, 151, 433, 727

Offset: 1

Harvey P. Dale, Oct 21 2011

Leading zeros are not permitted, so each term is 3 digits in length.

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

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812, A104824, A104825, A104826, A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198171, A198172, A198173, A198174, A198175, A104851, A198177.

Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]],3,1], IntegerLength[#]==3&&PrimeQ[#]&]

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A198165 Primes from merging of 5 successive digits in decimal expansion of sqrt(2).

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A198166 Primes from merging of 6 successive digits in decimal expansion of sqrt(2).

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A104845 Primes from merging of 4 successive digits in decimal expansion of e.

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A104846 Primes from merging of 5 successive digits in decimal expansion of e.

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A104848 Primes from merging of 7 successive digits in decimal expansion of e.

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A104849 Primes from merging of 8 successive digits in decimal expansion of e.

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A104851 Primes from merging of 10 successive digits in decimal expansion of e.

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A198167 Primes from merging of 7 successive digits in decimal expansion of sqrt(2).

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A198168 Primes from merging of 8 successive digits in decimal expansion of sqrt(2).