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

Author

Muniru A Asiru, Apr 18 2018

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Intersection of A006562 and A030431.

Cf. A303092, A303094, A303095.

Programs

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);

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 *)