const testCases = [

  ['1', true],

  ['1234', true],

  ['1221', true],

  ['3333', true],

  ['143332', true],

  ['22234', true],

  ['2234', true],

  ['22214', true],

  ['1221441', true],

  ['41233', true],

  ['13', false],

  ['1224', false],

  ['121', false],

  ['12221', false],

  ['43221', false]

];

const p=(s,d)=>(h=s[0],t=s.slice(1),g=t[0],!g||(d?g==h?p(t,-d):g%4==(h-d)%4&&p(t,d):p(s,1)||p(s,-1)));

​

testCases.forEach(c => {

  let e = c[1];

  let a = p(c[0]);

  console.log(c[0] + ': ' + (a === e ? 'pass' : `fail (expected ${e}, got ${a})`));

});

​

​