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A256076
Non-palindromic balanced primes.
7
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
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
KEYWORD
nonn,base
AUTHOR
Eric Angelini and M. F. Hasler, Mar 14 2015
STATUS
approved