Newman–Shanks–Williams-prímek

A matematikában egy Newman–Shanks–Williams-prím (NSW-prím) olyan p prímszám, ami felírható a következő alakban:

Az NSW-prímeket Morris Newman, Daniel Shanks és Hugh C. Williams írták le 1981-ben a négyzetszám rendű véges egyszerű csoportok tanulmányozása közben.

Az első néhány NSW-prím a 7, 41, 239, 9369319, 63018038201, … (A088165 sorozat az OEIS-ben), melyek a (A005850 sorozat az OEIS-ben) 3, 5, 7, 19, 29, … indexeinek felelnek meg.

A képlethez kötődő S sorozat sorozat a következő rekurzióval adható meg:

A sorozat első néhány eleme 1, 1, 3, 7, 17, 41, 99, … (A001333 sorozat az OEIS-ben). A sorozat minden tagja éppen fele a Pell-számoknak. A számok megjelennek a √2 konvergens lánctört-alakjában is.

Irodalom

  • Newman, M. (1980). „Simple groups of square order and an interesting sequence of primes”. Acta Arithmetica 38 (2), 129–140. o. 

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