A158128 -id:A158128 - cp's OEIS frontend

A062800 Primes of form 100*k + 1.

101, 401, 601, 701, 1201, 1301, 1601, 1801, 1901, 2801, 3001, 3301, 3701, 4001, 4201, 4801, 5101, 5501, 5701, 5801, 6101, 6301, 6701, 7001, 7901, 8101, 8501, 9001, 9601, 9901, 10301, 10501, 10601, 11701, 11801, 12101, 12301, 12401, 12601, 13001, 13901, 14401, 15101

Offset: 1

Jason Earls, Jul 19 2001

W. Dunham, Euler: The Master of Us All, The Mathematical Association of America, Washington, D.C., 1999, p. 78.

Harry J. Smith, Table of n, a(n) for n = 1..1000

Subsequence of primes of A158128.

Cf. A166457.

Select[100*Range[200]+1,PrimeQ] (* Harvey P. Dale, May 06 2018 *)

j=[]; for(n=1,400, if(isprime(100*n+1),j=concat(j,100*n+1))); j

{ n=0; for (m=1, 10^9, if (isprime(a=100*m + 1), write("b062800.txt", n++, " ", a); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 11 2009

a(n) = A158128(A166457(n)). - Elmo R. Oliveira, Feb 22 2025

A158127 a(n) = 100n^2 + 2n.

Original entry on oeis.org

102, 404, 906, 1608, 2510, 3612, 4914, 6416, 8118, 10020, 12122, 14424, 16926, 19628, 22530, 25632, 28934, 32436, 36138, 40040, 44142, 48444, 52946, 57648, 62550, 67652, 72954, 78456, 84158, 90060, 96162, 102464, 108966, 115668, 122570

Offset: 1

Vincenzo Librandi, Mar 13 2009

The identity (100*n + 1)^2 - (100*n^2 + 2*n)*10^2 = 1 can be written as A158128(n)^2 - a(n)*10^2 = 1. - Vincenzo Librandi, Feb 11 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(10^2*t+2)).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A158128.

I:=[102, 404, 906]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 11 2012

Table[100n^2 +2n,{n,45}]  (* Harvey P. Dale, Mar 15 2011 *)
LinearRecurrence[{3, -3, 1}, {102, 404, 906}, 50] (* Vincenzo Librandi, Feb 11 2012 *)

for(n=1, 50, print1(100*n^2 + 2*n", ")); \\ Vincenzo Librandi, Feb 11 2012

G.f.: x*(102 + 98*x)/(1-x)^3. - Vincenzo Librandi, Feb 11 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 11 2012

A180469 Primes of the form 100p + 1, where p is prime.

Original entry on oeis.org

701, 1301, 1901, 3701, 6101, 6701, 7901, 10301, 13901, 15101, 16301, 19301, 21101, 22901, 27701, 42101, 46301, 52301, 54101, 60101, 64301, 70901, 72701, 81101, 82301, 87701, 88301, 93701, 102101, 112901, 115301, 117101, 123701, 132701

Offset: 1

Kevin Batista (kevin762401(AT)yahoo.com), Sep 06 2010

			Example: 7*100 + 1 = 701 is prime, and is therefore a term.

Kevin Batista, Table of n, a(n) for n = 1..20000

Subsequence of A158128.

forprime(p=2,1e4,k=100*p+1;if(isprime(k),print1(k",")))

cp's OEIS Frontend

A062800 Primes of form 100*k + 1.

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A158127 a(n) = 100n^2 + 2n.

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A180469 Primes of the form 100p + 1, where p is prime.

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cp's OEIS Frontend

A062800 Primes of form 100*k + 1.

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Author

Keywords

References

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Mathematica

PARI

PARI

Formula

A158127 a(n) = 100*n^2 + 2*n.

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Author

Keywords

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Magma

Mathematica

PARI

Formula

A180469 Primes of the form 100p + 1, where p is prime.

Views

Author

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Examples

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Programs

PARI

A158127 a(n) = 100n^2 + 2n.