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Primes p such that p plus its decimal reversal is a cube.
1

%I #22 Apr 03 2023 10:36:13

%S 203993941,205399741,205795741,205993741,207894541,208795441,

%T 213399931,214498831,214795831,214894831,217498531,217894531,

%U 218993431,219894331,223597921,224399821,225795721,227498521

%N Primes p such that p plus its decimal reversal is a cube.

%C It is observed that 203993941 is the smallest prime in this sequence.

%H K. D. Bajpai and Giovanni Resta, <a href="/A226079/b226079.txt">Table of n, a(n) for n = 1..1000</a> (first 119 terms from K. D. Bajpai)

%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://t5k.org/curios/page.php?short=203993941"> Prime Curios! 203993941</a>

%e a(1) = 203993941: Reversing the digits gives 149399302 and 203993941+149399302=353393243=707^3.

%p with(StringTools):KD:= proc() local n,a,b,c,d,e,count;count:=1: for n from 1 to 17000000 do;a:=ithprime(n); b:=parse(Reverse(convert((a),string))); c:=a+b;d:=evalf(c^(1/3));e:=floor(d);if d=e then lprint(count,a);count:=count+1;fi ; od;end:KD();

%o (PARI) rev(n)=subst(Polrev(digits(n)),'x,10)

%o is(n)=isprime(n) && ispower(n+rev(n),3) \\ _Charles R Greathouse IV_, Aug 05 2013

%Y Cf. A059799 (similar sequence for squares), A080179.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Aug 05 2013