Why does the ADC return a sine wave?

Question

Arduino

Very strange ADC behavior. The task is to read the readings of several potentiometers and send them to another board (FPGA). I started by repeating the example www.arduino.cc/en/Tutorial/AnalogInOutSerial
However, difficulties arose - the diode blinks all the time at a frequency of about 3Hz, just like the values ​​​​changing from zero to 1023 and back come to the serial port

COM Port Console Readings

sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 52. output = 12
sensor = 51. output = 12
sensor = 99. output = 24
sensor = 193. output = 48
sensor = 322. output = 80
sensor = 467. output = 116
sensor = 576. output = 143
sensor = 684. output = 170
sensor = 814. output = 202
sensor = 916. output = 228
sensor = 1023. output = 255
sensor = 1023. output = 255
sensor = 1023. output = 255
sensor = 1023. output = 255
sensor = 929. output = 231
sensor = 778. output = 193
sensor = 603. output = 150
sensor = 295. output = 73
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0
sensor = 0. output = 0

Note that the potentiometer is not rotated.
I tried to repeat the experiment with other ports - the same thing. I decided to connect the port to the ground - to my surprise, the pattern repeated itself. Connecting to power through a 220 ohm resistor gave the same result.
However, if nothing is connected to the ADC input, some noise is output (approximately sensor = 300 ± 100). Tell me what could be the problem before I start exorcising the demons from the board.
PS About two years ago, exactly the same example worked as expected, i. correctly.

Scheme

in gland

The code

const int analogInPin = A4;  // Analog input pin that the potentiometer is attached to
const int analogOutPin = 9; // Analog output pin that the LED is attached to

int sensorValue = 0;        // value read from the pot
int outputValue = 0;        // value output to the PWM (analog out)

int a2 = 0;
int a3 = 0;
int a4 = 0;
int a5 = 0;

void setup() {
  // initialize serial communications at 9600 bps:
  Serial.begin(9600);
}

void loop() {

  // read the analog in value:
  sensorValue = analogRead(A1);
  a2 = analogRead(A2);
  a3 = analogRead(A3);
  a4 = analogRead(A4);
  a5 = analogRead(A5);

  outputValue = map(sensorValue, 0, 1023, 0, 255);
  analogWrite(analogOutPin, outputValue);

  // print the results to the serial monitor:
  Serial.print("a2 = " );
  Serial.print(a2);
  Serial.print("\t a3 = ");
  Serial.print(a3);
  Serial.print("\t a4 = ");
  Serial.print(a4);
  Serial.print("\t a5 = ");
  Serial.println(a5);

  delay(100);
}

Console output (tabs moved out)

a2 = 160.  a3 = 0. a4 = 0. a5 = 0
a2 = 92.    a3 = 0. a4 = 0. a5 = 0
a2 = 64.    a3 = 0. a4 = 0. a5 = 0
a2 = 55.    a3 = 0. a4 = 0. a5 = 0
a2 = 90.     a3 = 75. a4 = 90. a5 = 99
a2 = 207.   a3 = 340. a4 = 381. a5 = 425
a2 = 550. a3 = 934. a4 = 983. a5 = 1023
a2 = 766. a3 = 1023. a4 = 1023. a5 = 1023
a2 = 877. a3 = 1023. a4 = 1023. a5 = 1023
a2 = 928. a3 = 1023. a4 = 1023. a5 = 1023
a2 = 919. a3 = 953. a4 = 935. a5 = 920
a2 = 797. a3 = 696. a4 = 665. a5 = 631
a2 = 490. a3 = 179. a4 = 132. a5 = 85
a2 = 247. a3 = 6. a4 = 0. a5 = 0
a2 = 135. a3 = 0. a4 = 0. a5 = 0
a2 = 84. a3 = 0. a4 = 0. a5 = 0
a2 = 63. a3 = 0. a4 = 0. a5 = 0
a2 = 59. a3 = 0. a4 = 9. a5 = 25
a2 = 114. a3 = 129. a4 = 143. a5 = 158
a2 = 306. a3 = 519. a4 = 564. a5 = 610
a2 = 664. a3 = 1001. a4 = 1023. a5 = 1023
a2 = 823. a3 = 1023. a4 = 1023. a5 = 1023
a2 = 904. a3 = 1023. a4 = 1023. a5 = 1023
a2 = 936. a3 = 1023. a4 = 1023. a5 = 1023
a2 = 884. a3 = 874. a4 = 854. a5 = 834
a2 = 727. a3 = 560. a4 = 539. a5 = 498
a2 = 406. a3 = 74. a4 = 33. a5 = 0
a2 = 212. a3 = 0. a4 = 0. a5 = 0
a2 = 120. a3 = 0. a4 = 0. a5 = 0
a2 = 79. a3 = 0. a4 = 0. a5 = 0
a2 = 68. a3 = 0. a4 = 0. a5 = 0

Answer 1

By
One point there are two analog inputs (A0 and A1, although for testing you can plug all of them into one point for measurement, where the blue wire is painted on the potentiometer) and see what they read. If one jumps while the others are calm, then it is better not to use an inadequate analog input.
Ideally, all should show the same value.

Answer 2

I need a connection diagram
about noise on the ADC, these are ordinary pickups, this is normal if there is no pull-up