I'm not getting your approach to create the output - could you post your existing code?
Otherwise your definition of nearest (when number modulo 70 is not equal to zero) would help.
awk '
{
l=$1 % 70; if (! l ) c[NR]=d[NR]=1;
n[NR]=$1; m[NR]=l
}
END {
c[0]=d[0]=c[NR+1]=d[NR+1]=70;
for (i=0; i<NR; i++) if (m[i+1] <= m) c=1
for (i=NR; i>1; i--) if (m[i-1] <= m) d=1
for (i=1; i<=NR; i++) if (c && d) print n
}
' infile