A161165 The n-th twin prime plus the n-th isolated prime.

5, 28, 44, 58, 66, 84, 98, 112, 120, 138, 156, 186, 192, 228, 236, 268, 276, 318, 332, 370, 390, 406, 414, 456, 474, 498, 510, 528, 536, 580, 588, 606, 614, 648, 654, 670, 680, 712, 722, 786, 792, 868, 878, 898, 912, 948, 954, 1020, 1026, 1078, 1112, 1146, 1158, 1180

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 04 2009

Keywords

• nonn
• easy

Examples

			a(1) = 3 +  2 =  5;
a(2) = 5 + 23 = 28;
a(3) = 7 + 37 = 44.
		

Crossrefs

Cf. A001097, A007510.

Programs

Maple

isA001097 := proc(n) isprime(n) and (isprime(n+2) or isprime(n-2)) ; end proc:
A001097 := proc(n) if n = 1 then 3; else for p from procname(n-1)+2 by 2 do if isA001097(p) then return p end if; end do: end if; end proc:
isA007510 := proc(n) isprime(n) and not isprime(n+2) and not isprime(n-2) ; end proc:
A007510 := proc(n) if n = 1 then 2; else for p from procname(n-1)+1 do if isA007510(p) then return p end if; end do: end if; end proc:
A161165 := proc(n) A001097(n) + A007510(n) ; end proc:
seq(A161165(n),n=1..100) ; # R. J. Mathar, Mar 18 2010
# alternate program
isA001097 := proc(n) if isprime(n) then isprime(n+2) or isprime(n-2) ; else false; end if; end proc:
isA007510 := proc(n) if isprime(n) then not isprime(n+2) and not isprime(n-2) ; else false; end if; end proc:
A001097 := proc(n) option remember; if n = 1 then 3; else for a from procname(n-1)+1 do if isA001097(a) then return a; end if; end do: end if; end proc:
A007510 := proc(n) option remember; if n = 1 then 2; else for a from procname(n-1)+1 do if isA007510(a) then return a; end if; end do: end if; end proc:
A161165 := proc(n) A001097(n)+A007510(n) ; end proc: seq(A161165(n),n=1..90) ; # R. J. Mathar, Mar 29 2010

Formula

a(n) = A001097(n) + A007510(n).

Extensions

Entries checked by R. J. Mathar, Mar 18 2010