A131260 a(n) is the least palindrome > a(n-1) such that a(1) + a(2) + ... + a(n) is a semiprime.

4, 5, 6, 7, 11, 22, 66, 88, 202, 212, 242, 272, 404, 444, 464, 474, 595, 656, 707, 757, 777, 808, 828, 838, 868, 888, 969, 989, 1111, 1881, 2222, 2772, 3553, 4444, 5005, 5335, 5555, 5665, 5995, 6006, 6556, 6886, 8448, 8668, 8888, 9229, 9339, 10601

Offset: 1

Author

Jonathan Vos Post, Oct 20 2007

Keywords

• base
• easy
• nonn

Comments

Semiprime analog of A051934. The semiprime partial sums begin 4, 9, 15, 22, 33, 55, 121, 209, 411, 623, 865, 1137, 1541, 1985, 2449, 2923, - R. J. Mathar, Nov 09 2007

Examples

			a(3) = 6 because that is the smallest palindrome p such that 4+5+p is a semiprime, namely 4+5+6 = 15 = 3*5.
		

Crossrefs

Cf. A001358, A051934.

Programs

Maple

isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true ; else false; fi ; end: isA002113 := proc(n) local i,digs ; if n < 10 then true; else digs := convert(n,base,10) ; for i from 1 to nops(digs) do if op(i,digs) <> op(-i,digs) then RETURN(false) ; fi ; od: RETURN(true) ; fi ; end: A131260 := proc(n) option remember ; local a,i ; if n = 1 then 4; else for a from A131260(n-1)+1 do if isA002113(a) and isA001358( a+add(A131260(i),i=1..n-1) ) then RETURN(a) ; fi ; od: fi ; end: seq(A131260(n),n=1..70) ; # R. J. Mathar, Nov 09 2007

Mathematica

a = {4, 5}; Do[i = a[[ -1]] + 1; While[Not[FromDigits[Reverse[IntegerDigits[i]]] == i] || Not[Sum[FactorInteger[Plus @@ a + i][[j, 2]], {j, 1, Length[FactorInteger[ Plus @@ a + i]]}] == 2], i++ ]; AppendTo[a, i], {50}]; a (* Stefan Steinerberger, Nov 17 2007 *)

Extensions

Corrected and extended by R. J. Mathar and Stefan Steinerberger, Nov 09 2007