A113762 - OEIS

%I #13 Jun 27 2022 11:11:57

%S 21,31,51,71,121,142,161,162,164,181,211,237,326,343,412,416,456,491,

%T 494,612,616,726,817,929,1226,1228,1427,1513,1622,1776,1824,1828,1911,

%U 1915,1975,2127,2188,3716,5265,6276,6321,6491,6852,7739,14423,14487,15297,16159

%N Numbers n with nonzero digits in their decimal representation such that when all numbers formed by inserting the exponentiation symbol between any two digits are added up, the sum is prime.

%H Michael S. Branicky, <a href="/A113762/b113762.txt">Table of n, a(n) for n = 1..55</a>

%e a(6) = 142 because 1^42+14^2 = 197, which is prime.

%t lst = {}; Do[ If[ Min@ IntegerDigits@n > 0, a=0; p=10; While[(w = Floor[n/p]) > 0, a += w^ Mod[n, p]; p*=10]; If[PrimeQ[a], Print[{n, a}]; AppendTo[lst, n]]], {n, 11, 9999}]; lst

%o (Python)

%o from sympy import isprime

%o from itertools import count, islice, product

%o def agen():

%o     for d in count(2):

%o         for p in product("123456789", repeat=d):

%o             s = "".join(p)

%o             if isprime(sum(int(s[:i])**int(s[i:]) for i in range(1, d))):

%o                 yield int(s)

%o print(list(islice(agen(), 44))) # _Michael S. Branicky_, Jun 27 2022

%Y Cf. A117388.

%K base,nonn

%O 1,1

%A _Ray G. Opao_, Jan 18 2006

%E More terms from _Giovanni Resta_, Jan 19 2006

%E More terms from _Robert G. Wilson v_, Apr 27 2006

%E a(47) and beyond from _Michael S. Branicky_, Jun 27 2022