|
| |
|
|
A005098
|
|
Numbers n such that 4n+1 is prime.
|
|
25
| |
|
|
1, 3, 4, 7, 9, 10, 13, 15, 18, 22, 24, 25, 27, 28, 34, 37, 39, 43, 45, 48, 49, 57, 58, 60, 64, 67, 69, 70, 73, 78, 79, 84, 87, 88, 93, 97, 99, 100, 102, 105, 108, 112, 114, 115, 127, 130, 135, 139, 142, 144, 148, 150, 153, 154, 160, 163, 165, 168, 169, 175, 177, 183
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Sum of i-th and j-th triangular numbers, where i=A096029(n), j=A096030(n);i.e. a(n)=A000217(A096029(n)) + A000217(A096030(n)). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 16 2004
For every n in the sequence, there is exactly 1 square number that can be subtracted to leave a pronic (A002378). e.g. 27 - 25 = 2, 99 - 9 = 90. [From Jon Perry (jonperrydc(AT)btinternet.com), Nov 06 2010]
|
|
|
LINKS
| T. D. Noe and Moshe Levin, Table of n, a(n) for n = 1..10000 (First 1000 terms from T. D. Noe).
Eric Weisstein's World of Mathematics, Wilson's Theorem
|
|
|
FORMULA
| a(n)=(A002144(n)-1)/4.
|
|
|
MAPLE
| a := []; for n from 1 to 500 do if isprime(4*n+1) then a := [op(a), n]; fi; od: A005098 := n->a[n];
|
|
|
MATHEMATICA
| Select[Range[200], PrimeQ[4#+1]&] (* Harvey P. Dale, Apr 20 2011 *)
|
|
|
PROG
| (MAGMA) [n: n in [0..10000] | IsPrime(4*n+1)] [From Vincenzo Librandi, Nov 18 2010]
|
|
|
CROSSREFS
| See A002144 for the actual primes.
Cf. A002972, A002973, A173331, A173330. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2010]
Sequence in context: A066928 A032726 A029739 * A185661 A002977 A024799
Adjacent sequences: A005095 A005096 A005097 * A005099 A005100 A005101
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 26 2004
Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Mar 17 2010
|
| |
|
|
