A346215 a(n) is the start of the first maximal string of n consecutive primes such that the sum of squares of pairs of consecutive primes in the string is always divisible by 10.

2, 53, 7, 17, 347, 373, 3181, 431, 1511, 61, 2213, 14551, 32779, 12841, 23911, 31121, 1764349, 90001, 3037297, 5031121, 5934899, 17385223, 63052261, 23673281, 80690807, 1191279451, 7594193, 850110593, 300482639, 23554787897, 8785664509, 20835779213, 165645916039

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Example

a(4) = 17 because the four consecutive primes 17, 19, 23, 29 have 17^2 + 19^2, 19^2 + 23^2, 23^2 + 29^2 are all divisible by 10, and this is maximal because 13^2 + 17^2 and 29^2 + 31^2 are not divisible by 10.

Maple

P:= select(isprime, [2, seq(i, i=3..10^7, 2)]):
N:= nops(P):
R:= select(t -> P[t]^2 + P[t+1]^2 mod 10 = 0, [$1..N-1]):
nR:=nops(R):
V:= Vector(100): V[1]:= 2:
state:= 1: p:= P[R[1]];
for i from 2 to nR do
  if R[i] = R[i-1]+1 then state:= state+1
  else if V[state+1] = 0 then V[state+1]:= p fi;
       state:= 1;
       p:= P[R[i]];
  fi
od:
V:= convert(V, list):
member(0, V, 'm'):
V[1..m-1];

Crossrefs

Sequence in context: A248987 A179616 A200087 * A139841 A167771 A062853

Adjacent sequences: A346212 A346213 A346214 * A346216 A346217 A346218

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 22 2021

Extensions

a(22)-a(33) from Martin Ehrenstein, Sep 01 2021

Status

approved