A056028 Numbers k such that k^18 == 1 (mod 19^2).

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

Author

Robert G. Wilson v, Jun 08 2000

Keywords

• nonn
• easy

Links

• Matthew House, Table of n, a(n) for n = 1..10000
• 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).

Crossrefs

Cf. A056021, A056022, A056024, A056025, A056026, A056027.

Cf. A381319 (general case mod n^2).

Programs

Mathematica

x=19; Select[ Range[ 1250 ], PowerMod[ #, x-1, x^2 ]==1& ]

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

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

From Mike Sheppard, Feb 20 2025: (Start)

a(n) = a(n-18) + 19^2.

a(n) ~ (19^2/18)*n. (End)