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A338985 a(n) is the first prime p such that the sum of 2*n consecutive primes starting at p is an oblong number, or 0 if there is no such p. 3

%I

%S 5,13,3,13,37,137,139,283,7,37,31,73,41,457,67,757,2351,2591,43,1637,

%T 19,2437,157,5,881,4801,59,229,4349,2333,11,31,1759,1277,53,653,3109,

%U 307,373,4877,241,3719,3301,467,3517,197,1297,193,1033,941,2141,12041,601,599,1753,6317,4969,43,5153

%N a(n) is the first prime p such that the sum of 2*n consecutive primes starting at p is an oblong number, or 0 if there is no such p.

%C Conjecture: all a(n) > 0.

%H Robert Israel, <a href="/A338985/b338985.txt">Table of n, a(n) for n = 1..2845</a>

%e a(4) = 13 because the sum of the four consecutive primes starting at 13 is 13+17+19+23=72 which is the oblong number 8*9, and this is the first prime for which the sum is an oblong number.

%p N:= 10^5: P:= select(isprime,[2,seq(i,i=3..N,2)]):

%p S:= ListTools:-PartialSums([0,op(P)]):

%p nP:= nops(S):

%p f:= proc(n) local i;

%p for i from 1 to nP-n do

%p if issqr(1+4*(S[i+n]-S[i])) then return P[i] fi

%p od;

%p FAIL

%p end proc:

%p R:= NULL:

%p for i from 1 do

%p v:= f(2*i);

%p if v = FAIL then break fi;

%p R:= R, v

%p od:

%p R;

%Y Cf. A002378.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 20 2020

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Last modified May 22 06:54 EDT 2022. Contains 353933 sequences. (Running on oeis4.)