A100776 -id:A100776 - cp's OEIS frontend

A101086 Numbers k for which 997*k + 1009 is prime.

0, 6, 10, 12, 22, 36, 64, 76, 82, 94, 126, 130, 136, 144, 150, 162, 174, 186, 202, 204, 246, 250, 252, 274, 276, 292, 294, 300, 306, 312, 330, 342, 360, 364, 390, 430, 466, 472, 480, 484, 490, 502, 526, 540, 546, 582, 586, 592, 594, 606, 610, 616, 622, 642

Offset: 1

Parthasarathy Nambi, Jan 21 2005

nonn

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

			If k=6, then 997*6 + 1009 = 6991 (prime).
If k=10, then 997*10 + 1009 = 10979 (prime).
If k=12, then 997*12 + 1009 = 12973 (prime).

Cf. A100776, A101084, A101123, A101444.

[ n: n in [0..700] | IsPrime(997*n + 1009) ]; // Vincenzo Librandi, Feb 04 2011

Select[Range[0,700],PrimeQ[997#+1009]&] (* Harvey P. Dale, Jun 29 2011 *)

Extended by Ray Chandler, Jan 25 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

A101442 a(n) = 9973*n + 10007.

Original entry on oeis.org

10007, 19980, 29953, 39926, 49899, 59872, 69845, 79818, 89791, 99764, 109737, 119710, 129683, 139656, 149629, 159602, 169575, 179548, 189521, 199494, 209467, 219440, 229413, 239386, 249359, 259332, 269305, 279278, 289251, 299224, 309197, 319170, 329143, 339116

Offset: 0

Parthasarathy Nambi, Jan 18 2005

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

			If n=14, then 9973*14 + 10007 = 149629 (a prime).

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Chris Caldwell, The first 100,008 primes.
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A017029, A100775, A100776, A101444.

[9973*n + 10007: n in [0..50]]; // Vincenzo Librandi, Jul 14 2011

9973*Range[0,30]+10007 (* or *) LinearRecurrence[{2,-1},{10007,19980},40] (* Harvey P. Dale, Sep 02 2015 *)

a(n)=9973*n+10007 \\ Charles R Greathouse IV, Oct 16 2015

From Elmo R. Oliveira, Dec 07 2024: (Start)
G.f.: (10007 - 34*x)/(1 - x)^2.
E.g.f.: (10007 + 9973*x)*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)

Extended by Ray Chandler, Jan 25 2005

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A101086 Numbers k for which 997*k + 1009 is prime.

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

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A101442 a(n) = 9973*n + 10007.

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