A182404 -id:A182404 - cp's OEIS frontend

A210767 Numbers whose digit sum as well as sum of the 4th powers of the digits is a prime.

11, 12, 14, 16, 21, 23, 25, 29, 32, 34, 38, 41, 43, 47, 52, 58, 61, 67, 74, 76, 83, 85, 89, 92, 98, 101, 102, 104, 106, 110, 111, 113, 119, 120, 131, 133, 140, 146, 160, 164, 166, 179, 191, 197, 201, 203, 205, 209, 210, 223, 230, 232, 250, 269, 290, 296, 302

Offset: 1

Jonathan Vos Post, May 10 2012

This is to the exponent 4 as A182404 is to the exponent 2.

			21 is in the sequence because sum of digits 2+1= 3 is prime, and sum of the 4th powers of the digits 2^4+1^4=17 is a prime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A007953, A055013, A182404.

Select[Range[350],AllTrue[{Total[IntegerDigits[#]],Total[ IntegerDigits[ #]^4]},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 01 2019 *)

dspow(n,b,k)=my(s);while(n,s+=(n%b)^k;n\=b);s
select(n->isprime(sumdigits(n))&&isprime(dspow(n,10,4)), vector(10^3, i, i)) \\ Charles R Greathouse IV, May 11 2012

{n such that A055013(n) and A007953(n) are both primes}.

A245475 Numbers n such that the sum of digits, sum of squares of digits, and sum of cubes of digits are all prime.

Original entry on oeis.org

11, 101, 110, 111, 113, 131, 146, 164, 166, 199, 223, 232, 289, 298, 311, 322, 335, 337, 346, 353, 355, 364, 373, 388, 416, 436, 449, 461, 463, 494, 533, 535, 553, 566, 614, 616, 634, 641, 643, 656, 661, 665, 733, 829, 838, 883, 892, 919, 928, 944, 982, 991, 1001, 1010, 1011, 1013, 1031, 1046, 1064, 1066, 1099

Offset: 1

Derek Orr, Jul 23 2014

There are infinitely many numbers in this sequence; 0's can be added to any number any number of times in any logical order (i.e., the number doesn't start with a zero).

			1^1 + 4^1 + 6^1 = 11 is prime.
1^2 + 4^2 + 6^2 = 53 is prime.
1^3 + 4^3 + 6^3 = 281 is prime.
Thus 146, 164, 416, 461, 641, and 614 are members of this sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A182404, A225534, A108662.

filter:= proc(n) local L;
  L:= convert(n,base,10);
  isprime(convert(L,`+`)) and
  isprime(convert(map(`^`,L,2),`+`)) and
  isprime(convert(map(`^`,L,3),`+`))
end proc:
select(filter, [$1..2000]); # Robert Israel, Dec 04 2024

sdpQ[n_]:=Module[{idn=IntegerDigits[n]},AllTrue[{Total[idn], Total[ idn^2], Total[ idn^3]}, PrimeQ]]; Select[Range[1100],sdpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 06 2018 *)

for(n=1,10^3,d=digits(n);s1=sum(i=1,#d,d[i]);s2=sum(j=1,#d,d[j]^2);s3=sum(k=1,#d,d[k]^3);if(isprime(s1)&&isprime(s2)&&isprime(s3),print1(n,", ")))

cp's OEIS Frontend

A210767 Numbers whose digit sum as well as sum of the 4th powers of the digits is a prime.

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