A104843 -id:A104843 - cp's OEIS frontend

A198171 Primes from merging of 7 successive digits in decimal expansion of Pi forbidding leading zeros.

1592653, 6535897, 2643383, 5028841, 6939937, 3993751, 1170679, 8086513, 5822317, 1725359, 4930381, 2881097, 4612847, 3165271, 2712019, 1201909, 4914127, 1133053, 3841469, 1469519, 6951941, 9433057, 9326117, 4462379, 2749567, 5272489, 8912279, 8183011

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, A198167, A198168, A198169, A198170, A198172, A198173, A198174, A198175, A104851, A198177.

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

A198172 Primes from merging of 8 successive digits in decimal expansion of Pi forbidding leading zeros.

Original entry on oeis.org

28841971, 41971693, 82534211, 42117067, 30664709, 31725359, 49303819, 75648233, 37867831, 71201909, 48566923, 26648213, 13393607, 25409171, 57595919, 21861173, 81932611, 79962749, 24891227, 30119491, 40656643, 30860213, 39494639, 39522473, 98609437, 53921717

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, A198168, A198169, A198170, A198171, A198173, A198174, A198175, A104851, A198177.

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

A198173 Primes from merging of 9 successive digits in decimal expansion of Pi forbidding leading zeros.

Original entry on oeis.org

795028841, 502884197, 884197169, 971693993, 348253421, 421170679, 306647093, 812848111, 659334461, 233786783, 648566923, 346034861, 326648213, 829254091, 678925903, 959195309, 530921861, 938183011, 298336733, 798609437, 717629317, 320005681, 757789609

Offset: 1

Harvey P. Dale, Oct 21 2011

Leading zeros are not permitted, so each term is 9 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, A198170, A198171, A198172, A198174, A198175, A104851, A198177.

With[{len=9},Select[FromDigits/@Partition[RealDigits[Pi,10,1000][[1]], len,1],IntegerLength[#]==len&&PrimeQ[#]&]]

A198175 Primes from merging of 2 successive digits in decimal expansion of Pi.

Original entry on oeis.org

31, 41, 59, 53, 89, 97, 79, 23, 43, 83, 79, 41, 19, 97, 71, 37, 97, 59, 23, 89, 53, 11, 17, 67, 79, 13, 23, 47, 23, 31, 17, 53, 59, 11, 11, 17, 41, 19, 11, 59, 29, 89, 19, 97, 59, 61, 47, 23, 37, 67, 83, 31, 71, 19, 23, 61, 43, 13, 41, 73, 37, 31, 17, 29, 17

Offset: 1

Harvey P. Dale, Oct 21 2011

Leading zeros are not permitted, so each term is 2 digits in length.

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

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, A198170, A198171, A198172, A198173, A198174, A104851, A198177.

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

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

Original entry on oeis.org

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

A198776 Primes from merging of 2 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

53, 2, 43, 31, 59, 59, 23, 59, 5, 67, 23, 67, 67, 67, 47, 29, 17, 67, 31, 47, 7, 5, 83, 41, 17, 73, 97, 23, 53, 53, 3, 37, 29, 37, 73, 37, 73, 37, 67, 73, 79, 59, 47, 73, 3, 67, 53, 23, 31, 17, 61, 11, 11, 19, 7, 79, 47, 79, 37, 5, 2, 29, 13, 47, 61, 2, 29

Offset: 1

Harvey P. Dale, Oct 29 2011

Leading zeros are permitted, so some terms may be less than 2 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, A104936, A198161, A198162,
A198163, A198164, A198165, A198166, A198167, A198168, A198169,
A198170, A198171, A198172, A198173, A198175, A104851, A198177,
A198777, A198778, A198779, A198780, A198781, A198782,
A198783, A198784.

  egp[len_]:=Module[{egterms=FromDigits/@Partition[RealDigits[EulerGamma, 10, 1000][[1]],len,1]},Select[egterms,PrimeQ[#]&]];egp[2]
Select[FromDigits/@Partition[RealDigits[EulerGamma,10,500][[1]],2,1],PrimeQ] (* Harvey P. Dale, Mar 19 2020 *)

A198784 Primes from merging of 10 successive digits in decimal expansion of Euler-Mascheroni constant (in the order of appearance).

Original entry on oeis.org

7215664901, 1566490153, 3286060651, 6060651209, 9008240243, 4310421593, 2159335939, 9235988057, 8486772677, 8070824809, 2836224173, 3622417399, 3997644923, 33374293, 2582470949, 6008735203, 87352039, 3151776611, 5015079847, 7400299213, 3139925401, 3754139549

Offset: 1

Harvey P. Dale, Oct 29 2011

Leading zeros are permitted, so some terms are less than 10 digits in length.

See A104944 for the variant where no leading zeros are allowed. - M. F. Hasler, Nov 01 2014

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

For the Euler-Mascheroni constant, see also A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784 (this sequence) and A104944 (a variant).
For sqrt(2), see A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198161.
For e, see A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851.
For Pi, see A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174.
For the Golden Ratio, see A198177, A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812.

egp[len_]:=Module[{egterms=FromDigits/@Partition[RealDigits[EulerGamma, 10, 1000][[1]],len,1]},Select[egterms,PrimeQ[#]&]]; egp[10]

list_A198784(x=Euler,m=10)=m=10^m;for(k=1,default(realprecision),isprime(p=x\.1^k%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

A198777 Primes from merging of 3 successive digits in decimal expansion of Euler-Mascheroni constant.

Original entry on oeis.org

577, 431, 421, 593, 359, 593, 359, 677, 677, 467, 709, 947, 467, 463, 631, 809, 401, 283, 241, 173, 739, 997, 449, 353, 3, 337, 293, 937, 373, 733, 337, 773, 673, 739, 709, 491, 853, 233, 331, 151, 661, 211, 199, 79, 479, 937, 857, 2, 29, 547, 29, 43, 421

Offset: 1

Harvey P. Dale, Oct 29 2011

Leading zeros are permitted, so some terms are less than 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, A104937, A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198170, A198171, A198172, A198173, A198175, A104851, A198177, A198776, A198778, A198779, A198780, A198781, A198782, A198783, A198784.

egp[len_]:=Module[{egterms=FromDigits/@Partition[RealDigits[EulerGamma, 10, 1000][[1]],len,1]},Select[egterms,PrimeQ[#]&]]; egp[3]

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

Original entry on oeis.org

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 *)

cp's OEIS Frontend

A198171 Primes from merging of 7 successive digits in decimal expansion of Pi forbidding leading zeros.

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A198172 Primes from merging of 8 successive digits in decimal expansion of Pi forbidding leading zeros.

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A198173 Primes from merging of 9 successive digits in decimal expansion of Pi forbidding leading zeros.

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A198175 Primes from merging of 2 successive digits in decimal expansion of Pi.

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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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A198776 Primes from merging of 2 successive digits in decimal expansion of Euler-Mascheroni constant.

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A198784 Primes from merging of 10 successive digits in decimal expansion of Euler-Mascheroni constant (in the order of appearance).

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A198777 Primes from merging of 3 successive digits in decimal expansion of Euler-Mascheroni constant.

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

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