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A356051 a(n) is the index of the start of the first run of exactly n identical values in A356048. 0
5, 1, 103, 2683, 2831, 22031, 9105296 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(n) is the least k such that A356048(k) = ... = A356048(k+n-1) but these are different from A356048(k-1) (if k > 1) and A356048(k+n).
a(n) is the index k of the first of exactly n consecutive primes p such that the least primes q for which 2*q^2-p^2 is prime are all equal.
LINKS
EXAMPLE
a(3) = 103 as A356048(103) = A356048(104) = A356048(105) = 809, while A356048(102) = 811 and A356048(106) = 823 are different. Thus for prime(103) = 563, prime(104) = 569 and prime(105) = 571 we have 809^2 - 2*563^2 = 20543, 809^2 - 2*569^2 = 6959 and 809^2 - 2*571^2 = 2399 all prime.
MAPLE
f:= proc(n) local q;
q:= floor(sqrt(2)*n);
do
q:= nextprime(q);
if isprime(q^2-2*n^2) then return q fi;
od
end proc;
R:= Vector(6): count:= 0:
p:= 2: v:= f(2): c:= 1:
for k from 2 while count < 6 do
p:= nextprime(p);
w:= f(p);
if w = v then c:= c+1
else
if R[c] = 0 then R[c]:= k-c; count:= count+1 fi;
v:= w;
c:= 1;
fi
od:
convert(R, list);
CROSSREFS
Cf. A356048.
Sequence in context: A294258 A294260 A113114 * A099740 A362161 A359657
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Jul 24 2022
STATUS
approved

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Last modified March 1 11:39 EST 2024. Contains 370432 sequences. (Running on oeis4.)