login
A056028
Numbers k such that k^18 == 1 (mod 19^2).
11
1, 28, 54, 62, 68, 69, 99, 116, 127, 234, 245, 262, 292, 293, 299, 307, 333, 360, 362, 389, 415, 423, 429, 430, 460, 477, 488, 595, 606, 623, 653, 654, 660, 668, 694, 721, 723, 750, 776, 784, 790, 791, 821, 838, 849, 956, 967, 984, 1014, 1015, 1021, 1029
OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
FORMULA
a(n) = a(n-1) + a(n-18) - a(n-19). - Matthew House, Feb 12 2017
G.f.: x*(x^18 +27*x^17 +26*x^16 +8*x^15 +6*x^14 +x^13 +30*x^12 +17*x^11 +11*x^10 +107*x^9 +11*x^8 +17*x^7 +30*x^6 +x^5 +6*x^4 +8*x^3 +26*x^2 +27*x +1) / (x^19 -x^18 -x +1). - Colin Barker, Feb 12 2017
MATHEMATICA
x=19; Select[ Range[ 1250 ], PowerMod[ #, x-1, x^2 ]==1& ]
PROG
(PARI) isok(n) = Mod(n, 19^2)^18 == 1; \\ Michel Marcus, Feb 12 2017
(PARI) Vec(x*(x^18 +27*x^17 +26*x^16 +8*x^15 +6*x^14 +x^13 +30*x^12 +17*x^11 +11*x^10 +107*x^9 +11*x^8 +17*x^7 +30*x^6 +x^5 +6*x^4 +8*x^3 +26*x^2 +27*x +1) / (x^19 -x^18 -x +1) + O(x^100)) \\ Colin Barker, Feb 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Jun 08 2000
STATUS
approved