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A366310
First of a sequence of exactly n consecutive primes whose squares have the same last digit.
0
2, 13, 43, 157, 401, 2969, 7237, 30697, 57397, 68239, 576019, 967019, 225769, 6590069, 10942949, 21235127, 57401779, 186564317, 154836067, 117219967, 2598759227, 7470538489, 28594410847, 59107046659, 240456558467, 34511350409, 193861351357, 249423946921, 368059259143
OFFSET
1,1
COMMENTS
a(n) > 4.5*10^11 for n >= 30. - David A. Corneth, Oct 07 2023
EXAMPLE
a(3) = 43 because the 3 consecutive primes 43, 47, 53 all have squares ending in 9, while the primes 41 and 59 preceding 43 and following 53 have squares ending in 1.
MAPLE
N:= 16: # for a(1) .. a(N)
V:= Vector(N):
p:= 2: q:= 2: count:= 0: d:= 4: i:= 1:
while count < N do
p:= nextprime(p);
if p^2 mod 10 <> d then
if i <= N and V[i] = 0 then
V[i]:= q; count:= count+1;
fi;
q:= p; i:= 1; d:= p^2 mod 10;
else
i:= i+1;
fi
od:
convert(V, list);
PROG
(PARI)
upto(n) = {
my(res = [], ld = 4, streak = 1);
forprime(p = 3, n,
nd = p^2 % 10;
if(nd == ld,
streak++
,
if(streak > #res,
res = concat(res, vector(streak - #res, i, oo))
);
if(res[streak] == oo,
c = p;
for(i = 1, streak,
c = precprime(c-1);
);
res[streak] = c;
);
streak = 1;
);
ld = nd
); res
} \\ David A. Corneth, Oct 07 2023
CROSSREFS
Cf. A054681.
Sequence in context: A248198 A102296 A296807 * A308731 A025194 A084156
KEYWORD
nonn,base
AUTHOR
Robert Israel and the late J. M. Bergot, Oct 06 2023
EXTENSIONS
More terms from David A. Corneth, Oct 07 2023
STATUS
approved