login
A357190
a(n) is the least prime p such that A234575(p, A007953(p)) is the n-th power of a prime.
1
17, 13, 131, 107, 383, 613, 43607, 1021, 334403, 26099, 40637, 138967, 212867, 360049, 502210997, 2227399, 5682166613, 7339303, 13630913, 35650627, 92273957, 142605709, 4424729404133, 671087119, 42364430471219, 2684353351, 404156666702231, 10737417109, 4872756792902003
OFFSET
1,1
COMMENTS
a(n) is the least prime p such that the sum of the quotient and remainder on division of p by the sum of digits of p is the n-th power of an integer.
LINKS
EXAMPLE
a(3) = 131 because 131 is prime, has sum of digits 5, 131 = 26*5 + 1 and 26 + 1 = 27 = 3^3 where 3 is prime; and 131 is the least prime that works.
MAPLE
g:= proc(t, M) local s, q, r, n;
for s from 2 to 9*M do
for r from s-1 to 1 by -1 do
q:= t-r;
n:= q*s+r;
if convert(convert(n, base, 10), `+`) = s and isprime(n) then return n fi;
if n >= 10^M then return -1 fi;
od od;
-1
end proc:
G:= proc(m) local i, M, found, v, r;
found:= false; r:= infinity;
for M from 3 while not found do
for i from 1 while ithprime(i)^m < 10^M do
v:= g(ithprime(i)^m, M);
if v > 0 then found:= true; r:= min(v, r) fi
od od:
r
end proc:
map(G, [$1..30]);
CROSSREFS
Sequence in context: A089502 A279058 A373864 * A195534 A373469 A128158
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Oct 25 2022
STATUS
approved