A177929 a(1)=4. a(n+1) = a(n)+d-1, where d is the smallest prime divisor of (a(n)-1)*(a(n)+1).

4, 6, 10, 12, 22, 24, 28, 30, 58, 60, 118, 120, 126, 130, 132, 138, 274, 276, 280, 282, 562, 564, 568, 570, 1138, 1140, 1146, 1150, 1152, 2302, 2304, 2308, 2310, 4618, 4620, 4650, 9298, 9300, 9316, 9318, 9324, 9328, 9330, 9336, 9340, 9342, 18682, 18684

Offset: 1

Author

Vladimir Shevelev, May 15 2010

Keywords

• nonn

Crossrefs

Cf. A020639.

Programs

Maple

A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
A177929 := proc(n) local d1,d2; if n = 1 then 4; else d1 := A020639(procname(n-1)-1) ; d2 := A020639(procname(n-1)+1) ; procname(n-1)+min(d1,d2) -1; end if; end proc:
seq(A177929(n),n=1..52) ; # R. J. Mathar, May 31 2010

Mathematica

lpf[n_] := FactorInteger[n][[1, 1]];
a[n_] := a[n] = If[n == 1, 4, a[n-1]+lpf[a[n-1]^2-1]-1];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, May 13 2023 *)

Formula

a(n) = a(n-1) + A020639(a(n-1)^2 - 1) - 1. - R. J. Mathar, May 31 2010