A187828 Partition the sequence of consecutive primes into groups so that the absolute value of the alternating sum (-1)^n (An) with n = 0,....m in each group is prime.

3, 19, 37, 53, 71, 109, 149, 211, 251, 277, 307, 359, 397, 449, 479, 521, 593, 641, 709, 769, 823, 859, 919, 1009, 1033, 1087, 1171, 1217, 1277, 1321, 1367, 1399, 1459, 1549, 1609, 1637, 1693, 1747, 1879, 1973, 2039, 2099, 2213, 2341, 2399, 2437, 2531, 2663, 2777, 2879, 2939, 3061, 3251, 3433

Offset

1,1

Comments

From Robert Israel, Jun 24 2020: (Start)

The alternating sum must consist of more than two terms, and a(n) is the absolute value of that alternating sum.

Is the sequence increasing? For k <= 99999, a(k+1) >= a(k)+14. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(x) = Sum_{(-1)^n (An) with n = (0, 1, 2..m)}.

Example

a(1)=3 because the absolute value of the alternating sum (-1)^n (An) where An = (2, 3, 5, 7) with n = (0,1,2,3), is prime; a(2)=19 because the absolute value of the alternating sum (-1)^n (An) where An = (11, 13, 17, 19, 23) with n = (0, 1, 2, 3), is prime; a(3)=37 because the absolute value of the alternating sum (-1)^n (An) where An = (29, 31, 37, 41, 43) with n = (0, 1, 2, 3, 4) is prime.

Maple

p:= 1: R:= NULL:
for count from 1 to 50 do
  q:= nextprime(p); p:= nextprime(q); t:= q-p;
  e:= 1;
  do p:= nextprime(p);
     t:= t + e*p;
     e:= -e;
  until isprime(abs(t));
  R:= R, abs(t);
od:
R; # Robert Israel, Jun 23 2020

Crossrefs

Sequence in context: A062291 A106082 A283714 * A088786 A147237 A117674

Adjacent sequences: A187825 A187826 A187827 * A187829 A187830 A187831

Keyword

nonn

Author

Fabio Mercurio, Dec 27 2012

Extensions

More terms from Robert Israel, Jun 24 2020

Status

approved