A181103 -id:A181103

Search: a181103 -id:a181103

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A181737

Partial products of A181103.

+20
3

2, 6, 42, 546, 9282, 176358, 4056234, 117630786, 4822862226, 226674524622, 13373796952698, 1110025147073934, 98792238089580126, 9978016047047592726, 1067647717034092421682, 146267737233670661770434

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n+1)-a(n) is divisible by 6 for n > 1.

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

First three terms of A181103 are 2, 3, 7, so a(3) = 2*3*7 = 42.

PROG

(Magma) A181103:=function(n); S:=[2, 3]; if n le 2 then return S[n]; end if; p:=5; for k in [3..n] do while not IsPrime(Abs(S[k-2]+S[k-1]-p)) do p:=NextPrime(p); end while; Append(~S, p); if k eq n then return p; end if; p:=NextPrime(p); end for; end function; A181737:=function(n); S:=[ A181103(k): k in [1..n] ]; T:=[ m eq 1 select S[1] else Self(m-1)*S[m]: m in [1..n] ]; return T[n]; end function; [ A181737(n): n in [1..20] ]; // Klaus Brockhaus, Dec 19 2010

CROSSREFS

Cf. A181103.

KEYWORD

nonn,easy

AUTHOR

Giovanni Teofilatto

STATUS

approved

A181774

First differences of A181103.

+20
1

1, 4, 6, 4, 2, 4, 6, 12, 6, 12, 24, 6, 12, 6, 30, 36, 6, 60, 12, 6, 12, 24, 18, 36, 42, 30, 30, 18, 90, 6, 36, 42, 6, 54, 60, 48, 18, 12, 18, 30, 60, 6, 18, 6, 42, 30, 42, 18, 42, 12, 54, 12, 30, 42, 66, 42, 78, 36, 36, 12, 36, 12, 48, 66, 54, 24, 66, 24, 6

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

For a(n) > 4, a(n) is divisible by 6.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A181103(n+1) - A181103(n).

MAPLE

A181103 := proc(n) option remember: local p: if(n<=2)then return n+1: fi: p:=procname(n-1): do p:=nextprime(p): if(isprime(abs(p-procname(n-2)-procname(n-1))))then return p: fi: od: end: seq(A181103(n+1)-A181103(n), n=1..69); # Nathaniel Johnston, May 27 2011

MATHEMATICA

nxt[{a_, b_}]:=Module[{lp=NextPrime[b]}, While[!PrimeQ[Abs[a+b-lp]], lp = NextPrime[lp]]; {b, lp}]; Differences[NestList[nxt, {2, 3}, 70][[All, 1]]] (* Harvey P. Dale, Jul 26 2018 *)

KEYWORD

nonn,easy

AUTHOR

Giovanni Teofilatto

EXTENSIONS

More terms from Giovanni Teofilatto

STATUS

approved

A181729

Primes of the form A181737(k)+1.

+10
0

3, 7, 43, 547, 9283, 593966822339511354494269574612265371991631567

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The next term has 500 digits and is too large to be displayed here.

LINKS

Table of n, a(n) for n=1..6.

PROG

(Magma) z:=55; S:=[2, 3]; p:=5; for n in [3..z] do while not IsPrime(Abs(S[n-2]+S[n-1]-p)) do p:=NextPrime(p); end while; Append(~S, p); p:=NextPrime(p); end for; T:=[ n eq 1 select S[1] else Self(n-1)*S[n]: n in [1..#S] ]; [ p: n in [1..#T] | IsPrime(p) where p is T[n]+1 ]; // Klaus Brockhaus, Dec 19 2010

CROSSREFS

Cf. A181737, A181103.

KEYWORD

nonn

AUTHOR

Giovanni Teofilatto, Nov 16 2010

STATUS

approved

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