A139749 -id:A139749 - cp's OEIS frontend

A139751 Primes arising in A139749.

2, 3, 5, 7, 2, 3, 5, 7, 5, 7, 11, 13, 11, 13, 17, 17, 19, 23, 5

Offset: 1

Ctibor O. Zizka, May 19 2008

A178357 Numbers n such that d(1)^1 + d(2)^2 +...+ d(p)^p and d(1)^p + d(2)^p-1 +...+ d(p)^1 are prime numbers, where d(i), i=1..p, are the digits of n.

2, 3, 5, 7, 11, 12, 14, 16, 21, 23, 29, 32, 34, 38, 41, 43, 47, 56, 61, 65, 74, 83, 89, 92, 98, 101, 110, 111, 113, 115, 120, 122, 131, 133, 137, 139, 140, 146, 153, 155, 160, 164, 182, 186, 188, 191, 203, 205, 212, 214, 221, 225, 227, 230, 232, 236, 272, 281, 287, 290, 302, 304, 311, 313, 319, 320, 326, 331

Offset: 1

Michel Lagneau, Dec 21 2010

			1583 is in the sequence because :
1 + 5^2 + 8^3 + 3^4 = 619 and 1^4 + 5^3 + 8^2 + 3^1 = 193 are prime numbers.

Cf. A139749 A139750

with(numtheory):for n from 1 to 1000 do:l:=length(n):n0:=n:s1:=0:s2:=0:for
  m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :s1:=s1+u^(l-m+1):s2:=s2+u^m:od:
  if type(s1,prime)=true and type(s2,prime)=true then printf(`%d, `,n):else fi:od:

okQ[n_] := Module[{d=IntegerDigits[n], r}, r=Length[d]; PrimeQ[Total[d^Range[r]]] && PrimeQ[Total[d^Range[r, 1, -1]]]]; Select[Range[1000], okQ]

A330125 Positive integers whose digit-power sum is a prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 12, 14, 16, 21, 23, 25, 27, 32, 38, 41, 45, 49, 52, 54, 56, 58, 61, 65, 72, 78, 83, 85, 87, 94, 101, 110, 111, 113, 115, 122, 124, 128, 131, 139, 142, 146, 148, 151, 155, 164, 166, 182, 184, 193, 199, 212, 214, 218, 221, 223, 227, 232, 236, 238, 241

Offset: 1

Manan Shah, Dec 01 2019

Let M be an N-digit positive integer with digits (base 10) d_1, d_2, d_3, ..., d_N. If Sum_{i = 1..N} (d_i)^N is prime, then M is part of this sequence.
Numbers k such that A101337(k) is prime.
Both A139749 and A178357 are similar and match the first several terms of this sequence, but the digit powers are different. Additionally, perhaps a more interesting sequence is the subsequence of primes: 2, 3, 5, 7, 11, 23, 41, 61, 83.

			The first four terms are the single-digit primes; a(5) = 11 since 1^2 + 1^2 = 2, which is prime.

Robert Israel, Table of n, a(n) for n = 1..10000
Math Misery, Of Probes and Primes

Cf. A101337, A139749, A178357.

filter:= proc(n) local L,d,t;
   L:= convert(n,base,10);
   d:= nops(L);
   isprime(add(t^d, t=L))
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 17 2023

Select[Range[250], (d = IntegerDigits[#]; PrimeQ@ Total[d^Length[d]]) &] (* Giovanni Resta, Dec 02 2019 *)

isok(n) = {my(d = digits(n)); isprime(sum(k=1, #d, d[k]^#d));} \\ Michel Marcus, Dec 05 2019

More terms from Giovanni Resta, Dec 02 2019

A140281 A Diophantine equation over digits of n. Numbers n such that x_1/r +x_2/r-1 + ... + x_r/1 = k; x_i digits of n; k integer.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 320, 321, 322, 323, 324, 325, 326

Offset: 0

Ctibor O. Zizka, May 23 2008

			n=321 : 3/3 + 2/2 + 1/1 = 3, 321 belongs to the sequence

Cf. A005349, A137923, A138566, A139749, A139750, .

Join[{0},Select[Range[400],IntegerQ[Total[IntegerDigits[#]/Reverse[ Range[ IntegerLength[ #]]]]]&]] (* Harvey P. Dale, May 17 2016 *)

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A139751 Primes arising in A139749.

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A178357 Numbers n such that d(1)^1 + d(2)^2 +...+ d(p)^p and d(1)^p + d(2)^p-1 +...+ d(p)^1 are prime numbers, where d(i), i=1..p, are the digits of n.

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A330125 Positive integers whose digit-power sum is a prime.

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A140281 A Diophantine equation over digits of n. Numbers n such that x_1/r +x_2/r-1 + ... + x_r/1 = k; x_i digits of n; k integer.

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