A081677 -id:A081677 - cp's OEIS frontend

A246881 a(n)=A246880(n) where no k exists such that A246880(n)=A002277(k)(210^(A081677(k-1))+3).

609, 6660999, 666666609999999, 6666666660999999999, 66666666666666666099999999999999999, 666666666666666666666666609999999999999999999999999, 6666666666666666666666666660999999999999999999999999999

Offset: 1

Felix Fröhlich, Sep 06 2014

For any n there exists a k such that A246880(n)=A002277(k-1)*A173041(k).

Subsequence of A246880.

A173041 a(n) = 2*10^n + 3.

Original entry on oeis.org

5, 23, 203, 2003, 20003, 200003, 2000003, 20000003, 200000003, 2000000003, 20000000003, 200000000003, 2000000000003, 20000000000003, 200000000000003, 2000000000000003, 20000000000000003, 200000000000000003

Offset: 0

Vincenzo Librandi, Feb 08 2010

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11, -10).

Cf. A081677 (numbers n such that 2*10^n + 3 is prime), A101951 (numbers n such that 20*10^n + 3 is prime). - Klaus Brockhaus, Feb 28 2010

[2*10^n + 3: n in [0..20]]; // Vincenzo Librandi, Apr 05 2013

CoefficientList[Series[(5 - 32 x)/((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Apr 05 2013 *)
Table[2*10^n+3,{n,0,20}] (* Harvey P. Dale, Jun 01 2019 *)

G.f.: (5-32*x)/((1-x)*(1-10*x)). - Vincenzo Librandi, Apr 05 2013

A101951 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 27 for n > 0.

Original entry on oeis.org

0, 2, 4, 5, 6, 11, 15, 16, 21, 23, 34, 114, 119, 357, 1487, 1818, 4678, 9820, 27216, 27692, 194412

Offset: 1

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

Numbers n such that 20*10^n + 3 is prime.
Numbers n such that digit 2 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.
Numbers corresponding to terms <= 357 are certified primes.
a(21) > 10^5. - Robert Price, Nov 16 2014
a(22) > 2*10^5. - Robert Price, Jul 11 2015

			2003 is prime, hence 2 is a term.

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Makoto Kamada, Prime numbers of the form 200...003.

Cf. A000533, A002275, A081677.

[n: n in [0..500] | IsPrime(20*10^n+3)]; // Vincenzo Librandi, Nov 17 2014

Select[Range[0, 1000], PrimeQ[(20 10^# + 3)] &] (* Vincenzo Librandi, Nov 17 2014 *)

a=23;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)

for(n=0,1500,if(isprime(20*10^n+3),print1(n,",")))

a(n) = A081677(n+1) - 1. - Robert Price, Nov 16 2014

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(19)-a(20) derived from A081677 by Robert Price, Nov 16 2014
a(21) from Robert Price, Jul 11 2015

A101397 Numbers k such that 4*10^k+3 is prime.

Original entry on oeis.org

0, 1, 3, 7, 10, 40, 419, 449, 1737, 2245, 3131, 3813, 5345, 5659, 5681, 8410, 9097, 11293, 21061

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

nonn

See Kamada link for search limit and prime vs. PRP status.

a(20) > 2*10^5. - Robert Price, Jul 17 2015

			n = 1, 3, 7, 10 are members since 43, 4003, 40000003 and 40000000003 are prime numbers.

Makoto Kamada, Prime numbers of the form 400...003.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Cf. A049054, A081677, A056806, A101713.

Do[ If[ PrimeQ[4*10^n + 3], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Jan 18 2005 *)

is(n)=ispseudoprime(4*10^n+3) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = A101713(n-1) + 1.

a(18)-a(19) from Kamada data by Robert Price, Dec 10 2010

A086865 Numbers n such that 2*10^n+11 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 9, 19, 25, 39, 63, 133, 157, 274, 943, 1009, 1353, 7297, 16221, 25256, 30424, 52147

Offset: 1

Carl R. White, Aug 20 2003

a(22) > 10^5. - Robert Price, Jan 10 2015

Cf. A081677.

Do[ If[ PrimeQ[2*10^n + 11], Print[n]], {n, 0, 4800}]

is(n)=isprime(2*10^n+11) \\ Charles R Greathouse IV, Sep 27 2016

Edited and extended by Robert G. Wilson v, Aug 25 2003
Term a(13) (had been listed as 254) corrected by Jon E. Schoenfield, Jul 13 2010
a(17)-a(21) from Robert Price, Jan 10 2015

A101392 Numbers k such that 2*10^k+9 is prime.

Original entry on oeis.org

0, 1, 5, 25, 455, 761, 9205, 13561, 15955, 26669, 113941

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

761 and 9205 only probably prime. No others less than 10000.

a(12) > 2*10^5. - Robert Price, Jun 06 2015

			n = 1, 5 are members since 29 and 200009 are primes.

Makoto Kamada, Prime numbers of the form 200...009.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Cf. A081677, A088275, A101952.

Do[ If[ PrimeQ[2*10^n + 9], Print[n]], {n, 0, 10000}]

is(n)=ispseudoprime(2*10^n+9) \\ Charles R Greathouse IV, Jun 12 2017

a(n) = A101952(n-1) + 1 for n>1.

a(8)-a(9) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(10)-a(11) from Kamada data by Robert Price, Dec 13 2010
Prepended a(1)=0 by Robert Price, Jun 06 2015

A177134 Primes of the form 2*10^k + 3.

Original entry on oeis.org

5, 23, 2003, 200003, 2000003, 20000003, 2000000000003, 20000000000000003, 200000000000000003, 20000000000000000000003, 2000000000000000000000003, 200000000000000000000000000000000003

Offset: 1

Vincenzo Librandi, Dec 10 2010

nonn

Makoto Kamada, Prime numbers of the form 200...003.

Cf. A081677, A101951, A173041.

[ a: n in [0..250] | IsPrime(a) where a is 2*10^n + 3 ];

a(n) = A173041(A081677(n)).

A259541 Numbers n such that antisigma(n) is palindromic.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 13, 23, 30, 31, 36, 109, 119, 158, 351, 1645, 1653, 2003, 3476, 3520, 3934, 4913, 8037, 9379, 35324, 36516, 91951, 128955, 200003, 390066, 402603, 1068869, 2000003, 2144992, 2467458, 2867828, 3392245, 3607663

Offset: 1

Paolo P. Lava, Jun 30 2015

Primes of the form 2*10^k+3 belong the sequence (see A177134 and A081677).

			antisigma(1) = 1*2/2 - sigma(1) = 1 - 1 = 0;
antisigma(13) = 13*14/2 - sigma(13) = 91 - 14 = 77;
antisigma(109) = 109*110/2 - sigma(109) = 5995 - 110 = 5885.

Cf. A024816, A028980, A081677.

with(numtheory): T:=proc(w) local x, y, z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10);
od; y; end: P:=proc(q) local a,n;
for n from 1 to q do a:=n*(n+1)/2-sigma(n); if a=T(a) then print(n);
fi; od; end: P(10^9);

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; Select[Range@ 4000000, palQ[# (# + 1)/2 - DivisorSigma[1, #]] &] (* Michael De Vlieger, Jul 01 2015 *)

isok(n) = my(d = digits(n*(n+1)/2 - sigma(n))); Vecrev(d)==d; \\ Michel Marcus, Jul 01 2015

cp's OEIS Frontend

A246881 a(n)=A246880(n) where no k exists such that A246880(n)=A002277(k)*(2*10^(A081677(k-1))+3).

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A173041 a(n) = 2*10^n + 3.

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A101951 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 27 for n > 0.

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A101397 Numbers k such that 4*10^k+3 is prime.

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A086865 Numbers n such that 2*10^n+11 is prime.

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A101392 Numbers k such that 2*10^k+9 is prime.

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A177134 Primes of the form 2*10^k + 3.

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Magma

Formula

A259541 Numbers n such that antisigma(n) is palindromic.

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A246881 a(n)=A246880(n) where no k exists such that A246880(n)=A002277(k)(210^(A081677(k-1))+3).