A303093 Balanced primes of order one ending in 3.

53, 173, 263, 373, 563, 593, 653, 733, 1103, 1123, 1223, 1753, 2903, 2963, 3313, 3733, 4013, 4993, 5113, 5303, 5393, 5563, 6073, 6263, 6323, 6373, 6863, 7523, 7583, 7823, 8713, 9473, 10253, 10853, 11903, 11933, 12583, 12653, 12973, 13043, 13463, 14543, 14753

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

53 = (47 + 53 + 59)/3 = 159/3 and 53 = 5*10 + 3.

Maple

p:=ithprime: a:=n->`if`(add(p(n-k), k=-1..1)=3*p(n) and modp(p(n), 10) = 3, p(n), NULL): seq(a(n), n=3..2000);

Mathematica

Select[Partition[Prime[Range[2000]], 3, 1], Mean[#]==#[[2]]&&Mod[#[[2]], 10]==3&][[All, 2]] (* Harvey P. Dale, Apr 09 2022 *)

Prog

(GAP) P:=Filtered([1..15000], IsPrime);;
a:=Filtered(List(Filtered(List([0..Length(P)-3], k->List([1..3], j->P[j+k])), i->Sum(i)/3=i[2]), m->m[2]), l-> l mod 10=3);

Crossrefs

Intersection of A006562 and A030431.

Cf. A303092, A303094, A303095.

Sequence in context: A141880 A142698 A241044 * A056209 A098671 A056157

Adjacent sequences: A303090 A303091 A303092 * A303094 A303095 A303096

Keyword

nonn,base

Author

Muniru A Asiru, Apr 18 2018

Status

approved