A256076 Non-palindromic balanced primes.

1823, 1933, 2141, 2251, 2633, 2963, 3061, 3391, 4091, 4253, 4363, 4583, 5393, 5717, 5827, 6637, 6857, 6967, 7829, 8147, 8419, 8969, 9067, 9397, 14303, 14503, 15013, 15313, 15413, 15913, 16223, 16823, 17033, 17333, 18043, 18143, 18443, 18743, 19553, 19753, 19853

Offset

1,1

Comments

Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero. Palindromic primes (A002385) are "trivially" balanced, so they are excluded here.

These are the primes in A256075, see there for further information.

See A256081 for the binary version and A256090 for the hexadecimal version.

Links

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

Example

a(1)=1823 is balanced because 1*3/2 + 8*1/2 = 2*1/2 + 3*3/2.

Maple

filter:= proc(n) local L, m;
  L:= convert(n, base, 10);
  m:= (1+nops(L))/2;
add(L[i]*(i-m), i=1..nops(L))=0  and isprime(n) and L <> ListTools:-Reverse(L)
end proc:
select(filter, [seq(i, i=1001..20000, 2)]); # Robert Israel, May 29 2018

Prog

(PARI) is(n, d=digits(n), o=(#d+1)/2)=!(vector(#d, i, i-o)*d~)&&d!=Vecrev(d)&&isprime(n)

Crossrefs

Cf. A256075, A256081, A256090, A002385.

Sequence in context: A174770 A218104 A171349 * A179581 A230052 A234222

Adjacent sequences: A256073 A256074 A256075 * A256077 A256078 A256079

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Mar 14 2015

Status

approved