A101442 -id:A101442 - cp's OEIS frontend

A101444 Numbers k such that (9973*k + 10007) is a prime.

0, 14, 32, 42, 48, 98, 104, 108, 120, 122, 132, 180, 204, 210, 224, 228, 230, 264, 278, 300, 302, 308, 318, 342, 344, 348, 350, 374, 384, 402, 410, 414, 428, 438, 444, 462, 470, 500, 522, 540, 564, 602, 614, 638, 644, 672, 678, 692, 698, 714, 720, 740, 782

Offset: 1

Parthasarathy Nambi, Jan 18 2005

nonn

Note that 9973 is the largest four-digit prime and 10007 is the smallest five-digit prime.

			If k=14 then 9973*14 + 10007 = 149629 (prime).
If k=32 then 9973*32 + 10007 = 329143 (prime).
If k=42 then 9973*42 + 10007 = 428873 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A101123, A101084, A101086, A101442.

Select[ Range[ 0, 791], PrimeQ[9973# + 10007]&] (* Robert G. Wilson v, Jan 20 2005 *)

Extended by Lior Manor, Ray Chandler and Robert G. Wilson v, Jan 20 2005

A100775 a(n) = 97*n + 101.

Original entry on oeis.org

101, 198, 295, 392, 489, 586, 683, 780, 877, 974, 1071, 1168, 1265, 1362, 1459, 1556, 1653, 1750, 1847, 1944, 2041, 2138, 2235, 2332, 2429, 2526, 2623, 2720, 2817, 2914, 3011, 3108, 3205, 3302, 3399, 3496, 3593, 3690, 3787, 3884, 3981, 4078, 4175, 4272, 4369, 4466

Offset: 0

Parthasarathy Nambi, Jan 03 2005

Note that 97 is the largest two-digit prime and 101 is the smallest three-digit prime.

			If n=1, then 97*1 + 101 = 198.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A017029, A100776, A101084, A101442.

[97*n + 101: n in [0..50]]; // Vincenzo Librandi, Jul 14 2011

97*Range[0,50]+101 (* or *) LinearRecurrence[{2,-1},{101,198},50] (* Harvey P. Dale, Nov 26 2013 *)

a(n)=97*n+101 \\ Charles R Greathouse IV, Oct 16 2015

From Harvey P. Dale, Nov 26 2013: (Start)
a(n) = 2*a(n-1) - a(n-2); a(0)=101, a(1)=198.
G.f.: (101 - 4*x)/(x-1)^2. (End)
E.g.f.: exp(x)*(101 + 97*x). - Elmo R. Oliveira, Dec 08 2024

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005

Edited by Ray Chandler, Jan 25 2005

A100776 a(n) = 997*n + 1009.

Original entry on oeis.org

1009, 2006, 3003, 4000, 4997, 5994, 6991, 7988, 8985, 9982, 10979, 11976, 12973, 13970, 14967, 15964, 16961, 17958, 18955, 19952, 20949, 21946, 22943, 23940, 24937, 25934, 26931, 27928, 28925, 29922, 30919, 31916, 32913, 33910, 34907, 35904, 36901, 37898, 38895

Offset: 0

Parthasarathy Nambi, Jan 03 2005

Note that 997 is the largest three-digit prime and 1009 is the smallest four-digit prime.

			If n=1, 997*1 + 1009 = 2006.
If n=2, 997*2 + 1009 = 3003.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A017029, A100775, A101086, A101442.

[997 * n + 1009: n in [0..50]]; // Vincenzo Librandi, Jul 14 2011

A100776:=n->997 * n + 1009; seq(A100776(n), n=0..50); # Wesley Ivan Hurt, Jan 22 2014

Table[997 n + 1009, {n, 0, 50}] (* Wesley Ivan Hurt, Jan 22 2014 *)

a(n)=997*n+1009 \\ Charles R Greathouse IV, Jul 10 2016

From Elmo R. Oliveira, Dec 07 2024: (Start)
G.f.: (1009 - 12*x)/(1 - x)^2.
E.g.f.: (1009 + 997*x)*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005

Edited by Ray Chandler, Jan 25 2005

cp's OEIS Frontend

A101444 Numbers k such that (9973*k + 10007) is a prime.

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A100775 a(n) = 97*n + 101.

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A100776 a(n) = 997*n + 1009.

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