A092571 -id:A092571 - cp's OEIS frontend

A165724 Digit sums of A092571.

7, 13, 19, 55, 103, 121, 127, 163, 253, 391, 721, 793, 1063, 1441, 2719, 3313, 9595, 13045, 17863, 21889, 46243, 49891

Offset: 1

Parthasarathy Nambi, Sep 25 2009

Primes in this sequence are 7, 13, 19, 103, 127,163, ....

			The digit sum of 6666666666666666666666666666666666666666661 is 253.

Dario Alpern, Factorization using the Elliptic Curve Method

Cf. A007953, A056658, A092571.

a(n) = 1 + 6*A056658(n). [R. J. Mathar, Sep 25 2009]

a(n) = A007953(A092571(n)). - Michel Marcus, Jul 07 2023

More terms from R. J. Mathar, Sep 25 2009

A056658 Numbers k such that 60*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

1, 2, 3, 9, 17, 20, 21, 27, 42, 65, 120, 132, 177, 240, 453, 552, 1599, 2174, 2977, 3648, 7707, 8315, 10391, 12457, 21056, 26222, 48296, 64040, 84903, 92975, 95071

Offset: 1

Robert G. Wilson v, Aug 09 2000

Also numbers k such that (2*10^(k+1)-17)/3 is prime.

Makoto Kamada, Prime numbers of the form 66...661.
Index entries for primes involving repunits

Cf. A002275, A092571 (corresponding primes), A098088.

Do[ If[ PrimeQ[ 60*(10^n - 1)/9 + 1], Print[n]], {n, 7000}]

a(n) = A098088(n) - 1. - Robert Price, Aug 19 2014

1599 and 2174 (corresponding to probable primes) from Rick L. Shepherd, Feb 28 2004
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(23)-a(31) derived from A098088 by Robert Price, Aug 19 2014

A092675 Primes of the form 80*R_k + 1, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

881, 8888888888888888881, 8888888888888888888888888888888888888888888888888888888888888888888888888888881

Offset: 1

Rick L. Shepherd, Mar 02 2004

Primes of the form 888...881.
The number of 8's in each term is given by the corresponding term of A056664 and so the first term too large to include above is 888...8881 (with 138 8's).
Primes of the form (8*10^k - 71)/9. - Vincenzo Librandi, Nov 16 2010

Makoto Kamada, Prime numbers of the form 88...881.
Index entries for primes involving repunits

Cf. A056664 (corresponding k).

Cf. A051200, A004022, A093176, A093177, A089346, A093174, A092571.

Select[Table[10 FromDigits[PadRight[{},n,8]]+1,{n,150}],PrimeQ] (* Harvey P. Dale, Aug 07 2019 *)

A173805 a(n) = (6*10^n - 51)/9 for n > 0.

Original entry on oeis.org

1, 61, 661, 6661, 66661, 666661, 6666661, 66666661, 666666661, 6666666661, 66666666661, 666666666661, 6666666666661, 66666666666661, 666666666666661, 6666666666666661, 66666666666666661, 666666666666666661, 6666666666666666661, 66666666666666666661, 666666666666666666661

Offset: 1

Vincenzo Librandi, Feb 25 2010

Vincenzo Librandi, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A092571.

[(6*10^n-51)/9: n in [1..20]]; // Vincenzo Librandi, Jul 05 2012

CoefficientList[Series[(1+50*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* Vincenzo Librandi, Jul 05 2012 *)

a(n) = 10*a(n-1) + 51 with n > 0, a(0)=-5.
From Vincenzo Librandi, Jul 05 2012: (Start)
G.f.: x*(1+50*x)/((1-x)*(1-10*x)).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)
E.g.f.: 5 + exp(x)*(6*exp(9*x) - 51)/9. - Elmo R. Oliveira, Sep 09 2024

A109548 Primes of the form aaaa...aa1 where a is 1, 2, 3, 4 or 5.

Original entry on oeis.org

11, 31, 41, 331, 2221, 3331, 4441, 33331, 333331, 3333331, 33333331, 44444444441, 555555555551, 5555555555551, 222222222222222221, 333333333333333331, 1111111111111111111, 11111111111111111111111

Offset: 1

Roger L. Bagula, Jun 26 2005

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..38

Cf. A051200, A004022, A093176, A093177, A089346, A093174, A092571, A089345, A089347.

d[n_] = Mod[n, 6] a = Flatten[Table[Sum[d[k]*10^i, {i, 1, m}] + 1, {m, 1, 50}, {k, 1, 5}]] b = Flatten[Table[If[PrimeQ[a[[i]]] == True, a[[i]], {}], {i, 1, Length[a]}]]
Select[FromDigits/@Flatten[Table[PadLeft[{1},i,#]&/@{1,2,3,4,5},{i,2,80}],1],PrimeQ[#]&] (* Vincenzo Librandi, Dec 12 2011 *)

d=1, 2, 3, 4, 5 a(n) = if prime then Sum[d*10^i, {i, 1, m}] + 1

A109549 Primes of the form aaaa...aa1 where a is 6, 7, 8 or 9.

Original entry on oeis.org

61, 71, 661, 881, 991, 6661, 99991, 9999991, 6666666661, 7777777777771, 666666666666666661, 8888888888888888881, 77777777777777777771, 666666666666666666661, 6666666666666666666661, 77777777777777777777771

Offset: 1

Roger L. Bagula, Jun 26 2005

nonn

Easy-to-remember large primes can be formed in this manner.

Vincenzo Librandi, Table of n, a(n) for n = 1..43

Cf. A051200, A004022, A093176, A093177, A089346, A093174, A092571, A089345, A089347.

d[n_] = If[5 + Mod[n, 6] > 0, 5 + Mod[n, 6], 1] a = Flatten[Table[Sum[d[k]*10^i, {i, 1, m}] + 1, {m, 1, 50}, {k, 1, 4}]] b = Flatten[Table[If[PrimeQ[a[[i]]] == True, a[[i]], {}], {i, 1, Length[a]}]]
Select[FromDigits/@Flatten[Table[PadLeft[{1},i,#]&/@{6,7,8,9},{i,2,100}],1],PrimeQ[#]&] (* Vincenzo Librandi, Dec 12 2011 *)

d=6, 7, 8, 9 a(n) = if prime then Sum[d*10^i, {i, 1, m}] + 1

A109550 Primes of the form aaaa...aa1 where a is 3, 4, 5, 6 or 7.

Original entry on oeis.org

31, 41, 61, 71, 331, 661, 3331, 4441, 6661, 33331, 333331, 3333331, 33333331, 6666666661, 44444444441, 555555555551, 5555555555551, 7777777777771, 333333333333333331, 666666666666666661, 77777777777777777771

Offset: 1

Roger L. Bagula, Jun 26 2005

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..52

Cf. A051200, A004022, A093176, A093177, A089346, A093174, A092571, A089345, A089347.

d[n_] = If[2 + Mod[n, 6] > 0, 2 + Mod[n, 6], 1] a = Flatten[Table[Sum[d[k]*10^i, {i, 1, m}] + 1, {m, 1, 50}, {k, 1, 4}]] b = Flatten[Table[If[PrimeQ[a[[i]]] == True, a[[i]], {}], {i, 1, Length[a]}]]
Select[FromDigits/@Flatten[Table[PadLeft[{1},i,#]&/@{3,4, 5,6,7},{i,2,100}],1],PrimeQ[#]&] (* Vincenzo Librandi, Dec 12 2011 *)

d=3, 4, 5, 6, 7 a(n) = if prime then Sum[d*10^i, {i, 1, m}] + 1

A160452 Invertible primes of the form 1 followed by a string of 9's.

Original entry on oeis.org

19, 199, 1999, 1999999999999999999999999999

Offset: 1

Lekraj Beedassy, May 14 2009

These are values in A055558 whose rotation by 180 degrees occurs in A092571. I have checked all the numbers that correspond to entries in A002957 and can confirm that the next term in this sequence, if it exists, is greater than 2*10^55347-1. [From Dmitry Kamenetsky, May 22 2009]

			1999, for instance, is a prime which rotated upside down through 180 degrees becomes the prime 6661. Hence 1999 is in the sequence.

Cf. A048890, A055558.

Cf. A092571, A002957. [From Dmitry Kamenetsky, May 22 2009]

cp's OEIS Frontend

A165724 Digit sums of A092571.

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A056658 Numbers k such that 60*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

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A092675 Primes of the form 80*R_k + 1, where R_k is the repunit (A002275) of length k.

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A173805 a(n) = (6*10^n - 51)/9 for n > 0.

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A109548 Primes of the form aaaa...aa1 where a is 1, 2, 3, 4 or 5.

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A109549 Primes of the form aaaa...aa1 where a is 6, 7, 8 or 9.

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A109550 Primes of the form aaaa...aa1 where a is 3, 4, 5, 6 or 7.

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A160452 Invertible primes of the form 1 followed by a string of 9's.

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