A366310 First of a sequence of exactly n consecutive primes whose squares have the same last digit.

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

Author

Robert Israel and the late J. M. Bergot, Oct 06 2023

Keywords

• nonn
• base

Comments

a(n) > 4.5*10^11 for n >= 30. - David A. Corneth, Oct 07 2023

Examples

			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.
		

Crossrefs

Cf. A054681.

Programs

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);

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

Extensions

More terms from David A. Corneth, Oct 07 2023