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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A174770 A218104 A171349 * A179581 A230052 A234222
KEYWORD
nonn,base
AUTHOR
Eric Angelini and M. F. Hasler, Mar 14 2015
STATUS
approved

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Last modified May 30 07:51 EDT 2023. Contains 363050 sequences. (Running on oeis4.)