|
|
A307315
|
|
Primes p such that p + A007953(p) is the square of a prime.
|
|
1
|
|
|
2, 17, 347, 521, 10601, 32027, 39569, 58061, 62969, 100469, 109541, 120401, 398129, 426383, 434261, 829883, 896771, 935063, 1190261, 1216583, 1261109, 1559963, 1697771, 2105381, 2128649, 2505857, 2778851, 2886563, 2920649, 3051977, 3157703, 3636617, 4068257, 5139257, 5480249, 5650097, 5938931
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
All terms == 2 (mod 3).
More than one prime p can have the same value of p + A007953(p), e.g. 528677993 + A007953(52867793) = 528678011 + A007953(528678011) = 22993^2.
|
|
LINKS
|
|
|
EXAMPLE
|
a(3)= 347 is in the sequence because 347+3+4+7=361=19^2 and 347 and 19 are primes.
|
|
MAPLE
|
f:= proc(q) local m, d, nmin;
m:= q^2;
d:= ilog10(m)+1;
nmin:= m - 9*d;
nmin:= nmin + ((5-nmin) mod 6);
op(select(t -> t + convert(convert(t, base, 10), `+`)=m and isprime(t), {seq(n, n=nmin .. m-2, 6)}))
end proc:
f(2):= 2:
sort(map(f, [seq(ithprime(i), i=1..2000)]));
|
|
PROG
|
(PARI) is(n) = my(x=n+sumdigits(n)); isprimepower(x)==2
forprime(p=1, 6e6, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Apr 02 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|