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

1,1

Comments

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

Links

Table of n, a(n) for n=1..29.

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

Adjacent sequences: A366307 A366308 A366309 * A366311 A366312 A366313

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