A210110 Primes p such that 2p*(p+1) is the sum of 2 successive primes.

2, 3, 5, 7, 23, 29, 41, 59, 79, 89, 101, 131, 139, 151, 197, 229, 317, 337, 347, 389, 397, 421, 479, 631, 743, 761, 821, 829, 953, 977, 1033, 1193, 1279, 1451, 1697, 1747, 1787, 1789, 1879, 1997, 1999, 2017, 2099, 2213, 2237, 2347, 2411, 2477, 2579, 2621, 2663

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

2 is in the sequence because 2*2*(2+1) = 5+7 = 12.
3 is in the sequence because 2*3*(3+1) = 11+13 = 24.
5 is in the sequence because 2*5*(5+1) = 29+31 = 60.
7 is in the sequence because 2*7*(7+1) = 53+59 = 112.
23 is in the sequence because 2*23*(23+1) = 547+557 = 1104.

Maple

a:= proc(n) option remember; local p, t;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         t:= p*(p+1);
         if prevprime(t)+nextprime(t)=2*t then return p fi
      od
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, Mar 19 2012

Mathematica

a[n_] := a[n] = Module[{p, t}, p = If[n==1, 1, a[n-1]]; While[True, p = NextPrime[p]; t = p(p+1); If[NextPrime[t, -1] + NextPrime[t]==2t, Return[p]]]];
Array[a, 60] (* Jean-François Alcover, Nov 20 2020, after Alois P. Heinz *)

Crossrefs

Cf. A001043.

Sequence in context: A225659 A068690 A069556 * A235144 A235126 A309248

Adjacent sequences: A210107 A210108 A210109 * A210111 A210112 A210113

Keyword

nonn

Author

Gerasimov Sergey, Mar 17 2012

Status

approved