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Sum-of-digits of k appears somewhere in prime(k).
3

%I #17 Jul 03 2021 10:56:29

%S 7,12,13,21,25,28,30,45,47,72,81,100,104,106,107,108,114,123,133,143,

%T 150,151,152,162,171,172,180,181,191,200,207,214,230,239,249,259,269,

%U 278,279,288,298,312,314,319,322,333,340,342,344,359,397,400,403,405

%N Sum-of-digits of k appears somewhere in prime(k).

%C Sums-of-digits of m are in A075697, primes are in A075698.

%H Michael S. Branicky, <a href="/A075696/b075696.txt">Table of n, a(n) for n = 1..10000</a>

%e 12 is a term because sum-of-digits(12)=1+2=3 appears in prime(12)=37.

%e 191 is a term because sum-of-digits(191)=1+9+1=11 appears in prime(191)=1153.

%t Select[Range@500,StringContainsQ[ToString@Prime@#,ToString@Total@IntegerDigits@#]&] (* _Giorgos Kalogeropoulos_, Jul 03 2021 *)

%o (Python)

%o from sympy import prime, primerange

%o def auptopn(lim):

%o alst = []

%o for k, pk in enumerate(primerange(2, prime(lim)+1), start=1):

%o if str(sum(map(int, str(k)))) in str(pk): alst.append(k)

%o return alst

%o print(auptopn(405)) # _Michael S. Branicky_, Jul 03 2021

%Y Cf. A075697, A075698.

%K easy,nonn,base

%O 1,1

%A _Zak Seidov_, Sep 26 2002

%E Corrected and extended by _Sascha Kurz_, Jan 30 2003