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Primes of the form k + A037276(k).
3

%I #17 Feb 06 2021 22:09:26

%S 2,29,41,233,239,251,257,269,293,311,359,383,401,419,449,467,491,2269,

%T 2309,2339,2377,2381,2393,2411,2417,2447,2473,2503,2543,2579,2591,

%U 2621,2633,2671,2687,2699,2713,2753,2789,2797,2819,2843,2879,2939,3011,3041,3067,3083,3119,3137,3167,3191,3203

%N Primes of the form k + A037276(k).

%C All terms have first digit 2, 3 or 4.

%H Robert Israel, <a href="/A340633/b340633.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 2 = 1 + A037276(1) = 1 + 1;

%e a(2) = 29 = 6 + A037276(6) = 6 + 23;

%e a(3) = 41 = 14 + A037276(14) = 14 + 27;

%e a(4) = 233 = 22 + A037276(22) = 22 + 211;

%e a(5) = 251 = 18 + A037276(18) = 18 + 233

%e = 34 + A037276(34) = 34 + 217.

%p N:= 5000: # for terms <= N

%p dcat:= proc(L) local i, x;

%p x:= L[-1];

%p for i from nops(L)-1 to 1 by -1 do

%p x:= 10^(1+ilog10(x))*L[i]+x

%p od;

%p x

%p end proc:

%p A037276:= proc(n) local F;

%p F:= sort(ifactors(n)[2], (a, b) -> a[1] < b[1]);

%p dcat(map(t -> t[1]$t[2], F));

%p end proc:

%p A037276(1):= 1:

%p R:= NULL:

%p for n from 1 to N/2 do

%p v:= n + A037276(n);

%p if v < N and isprime(v) then R:= R, v fi;

%p od:

%p sort(convert({R},list));

%Y Cf. A037276, A340634, A340636.

%K nonn,look,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 13 2021