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A113762 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.

%I A113762 #13 Jun 27 2022 11:11:57
%S A113762 21,31,51,71,121,142,161,162,164,181,211,237,326,343,412,416,456,491,
%T A113762 494,612,616,726,817,929,1226,1228,1427,1513,1622,1776,1824,1828,1911,
%U A113762 1915,1975,2127,2188,3716,5265,6276,6321,6491,6852,7739,14423,14487,15297,16159
%N A113762 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 A113762 Michael S. Branicky, <a href="/A113762/b113762.txt">Table of n, a(n) for n = 1..55</a>
%e A113762 a(6) = 142 because 1^42+14^2 = 197, which is prime.
%t A113762 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 A113762 (Python)
%o A113762 from sympy import isprime
%o A113762 from itertools import count, islice, product
%o A113762 def agen():
%o A113762     for d in count(2):
%o A113762         for p in product("123456789", repeat=d):
%o A113762             s = "".join(p)
%o A113762             if isprime(sum(int(s[:i])**int(s[i:]) for i in range(1, d))):
%o A113762                 yield int(s)
%o A113762 print(list(islice(agen(), 44))) # _Michael S. Branicky_, Jun 27 2022
%Y A113762 Cf. A117388.
%K A113762 base,nonn
%O A113762 1,1
%A A113762 _Ray G. Opao_, Jan 18 2006
%E A113762 More terms from _Giovanni Resta_, Jan 19 2006
%E A113762 More terms from _Robert G. Wilson v_, Apr 27 2006
%E A113762 a(47) and beyond from _Michael S. Branicky_, Jun 27 2022