A158217 -id:A158217 - cp's OEIS frontend

A158473 Primes whose digit sum contains one or more digits of the same prime.

2, 3, 5, 7, 19, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 271, 281, 283, 307, 317, 337, 347, 367, 373, 379, 397, 419, 461, 463, 467, 491, 541, 557, 571, 613, 617, 619, 631, 641, 643, 647, 661, 673, 691, 719, 733, 739, 743, 751

Offset: 1

Parthasarathy Nambi, Mar 20 2009

			139 is a prime whose digit sum of 13 contains the digits 1 and 3 which are also in the prime.
149 is a prime whose digit sum of 14 contains the digits 1 and 4 which are also in the prime.
419 is a prime whose digit sum of 14 contains the digits 1 and 4 which are also in the prime.

Robert Israel, Table of n, a(n) for n = 1..10000
Chris Caldwell, The First 1,000 Primes

Cf. A107579, A158217, A158293.

filter:= proc(n) local L,s;
  L:= convert(n,base,10);
  s:= convert(L,`+`);
  convert(convert(s,base,10),set) intersect convert(L,set) <> {}
end proc:
select(filter, [seq(ithprime(i),i=1..100)]); # Robert Israel, Feb 27 2023

isok(p) = isprime(p) && (#setintersect(Set(digits(p)), Set(digits(sumdigits(p)))) >= 1); \\ Michel Marcus, Nov 12 2017

Single-digit primes added by R. J. Mathar, Jul 08 2009

Typos in data corrected by D. S. McNeil and Andrew Weimholt, Aug 17 2010

A158571 Primes whose digit sum is a single-digit nonprime.

Original entry on oeis.org

13, 17, 31, 53, 71, 103, 107, 211, 233, 251, 431, 503, 521, 701, 1021, 1061, 1151, 1201, 1223, 1511, 1601, 2011, 2141, 2213, 2411, 3001, 3023, 3041, 3203, 3221, 4013, 4211, 5003, 5021, 6011, 6101, 7001, 10007, 10061, 10111, 10133, 10151, 10223, 10313

Offset: 1

Parthasarathy Nambi, Mar 21 2009

It is interesting to observe that it is hard to find (I found none) primes whose digit sum is 6. On the contrary, it is easier to find primes whose digit sum is 8.

The digit sum 6 does not occur here because a number with digit sum 6 is divisible by 3 and therefore not prime. - R. J. Mathar, Mar 26 2009

			1061 is a prime whose digit sum is 8, which is a single-digit nonprime.

Robert Israel, Table of n, a(n) for n = 1..10000
Chris Caldwell, The First 1,000 Primes

Cf. A158217.

for i from 1 to 8 do if member(i,[1,3,7]) then S[1,i]:= {i} else S[1,i]:= {} fi od:
for d from 2 to 5 do
  for x from 1 to 8 do
    S[d,x]:= {};
    for y from 0 to x-1 do
      S[d,x]:= S[d,x] union map(t -> 10^(d-1)*y + t, S[d-1,x-y])
od od od:
select(isprime, S[5,4] union S[5,8]); # Robert Israel, Apr 14 2021

Union of A062339 and A062343. - R. J. Mathar, Mar 26 2009

Extended by R. J. Mathar, Mar 26 2009

cp's OEIS Frontend

A158473 Primes whose digit sum contains one or more digits of the same prime.

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