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

1,1

Links

Table of n, a(n) for n=1..54.

Formula

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

Example

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

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

Crossrefs

Cf. A001097, A007510.

Sequence in context: A218346 A106679 A341061 * A063140 A316560 A275709

Adjacent sequences: A161162 A161163 A161164 * A161166 A161167 A161168

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jun 04 2009

Extensions

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

Status

approved