cp's OEIS Frontend

A340537 Primes that are sums of a sequence of consecutive terms of A006094.

%I A340537 #18 Jan 11 2021 10:50:45
%S A340537 127,491,1201,1427,2003,2713,2767,5431,7229,7639,13001,17231,18061,
%T A340537 20753,24509,37337,37589,38149,38261,44563,44839,50969,51517,53609,
%U A340537 55201,60859,76519,77191,80239,80783,81703,90823,91583,96493,103079,103687,110573,126713,130411,134093,137777,139199,139663
%N A340537 Primes that are sums of a sequence of consecutive terms of A006094.
%C A340537 Each term is the sum of at least three consecutive terms of A006094.
%C A340537 A number that can be expressed as such a sum in more than one way is only listed once.  The first such number is 50911291 = 547*557+...+1051*1061 = 1423*1427+...+1559*1567.
%H A340537 Robert Israel, <a href="/A340537/b340537.txt">Table of n, a(n) for n = 1..10000</a>
%e A340537 a(1) = 5*7+7*11+11*13 = 127.
%e A340537 a(2) = 5*7+7*11+11*13+13*17+17*19 = 491.
%e A340537 a(3) = 11*13+13*17+17*19+19*23+23*29 = 1201.
%e A340537 a(4) = 19*23+23*29+29*31 = 1427.
%p A340537 SP:= [seq(ithprime(i)*ithprime(i+1),i=1..100)]:
%p A340537 SSP:= ListTools:-PartialSums([0,op(SP)]):
%p A340537 select(t -> t <= SP[-1] and isprime(t),
%p A340537   {seq(seq(SSP[j]-SSP[i],i=1..j-3),j=4..nops(SSP))});
%Y A340537 Cf. A006094, A340465.  Includes A287653.
%K A340537 nonn
%O A340537 1,1
%A A340537 _J. M. Bergot_ and _Robert Israel_, Jan 10 2021