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A308821 Semiprimes where the sum of the digits equals the difference between the prime factors.

%I A308821 #25 Sep 08 2022 08:46:21
%S A308821 14,95,527,851,1247,3551,4307,8051,14351,26969,30227,37769,64769,
%T A308821 87953,152051,163769,199553,202451,256793,275369,341969,455369,
%U A308821 1070969,1095953,1159673,1232051,1625369,1702769,2005007,2081993
%N A308821 Semiprimes where the sum of the digits equals the difference between the prime factors.
%C A308821 14 is the only even number in the sequence, since 2 is the only even prime and p-2 grows much faster than the digit sum of 2p.
%H A308821 James Beyer, <a href="/A308821/b308821.txt">Table of n, a(n) for n = 1..1000</a>
%H A308821 James Beyer, <a href="https://jebeyer.github.io/nlfourteen.html">Numbers Like Fourteen</a>
%H A308821 Wikipedia, <a href="https://en.wikipedia.org/wiki/Digit_sum">Digit sum</a>
%H A308821 Wikipedia, <a href="https://en.wikipedia.org/wiki/Semiprime">Semiprime</a>
%e A308821 14=2*7 and 1+4=7-2.
%e A308821 95=5*19 and 9+5=19-5.
%e A308821 527=17*31 and 5+2+7=31-17.
%t A308821 Take[Sort@ Reap[ Do[ If[PrimeQ[q + g] && g == Total@ IntegerDigits[n = q (q + g)], Sow@n], {g, 9*9}, {q, Prime@ Range@ 2000}]][[2, 1]], 100] (* _Giovanni Resta_, Jul 25 2019 *)
%t A308821 spdpfQ[n_]:=Module[{f=FactorInteger[n][[All,1]]},PrimeOmega[n]== 2 && Total[ IntegerDigits[n]]==f[[2]]-f[[1]]]; Select[Range[ 21*10^5],spdpfQ]// Quiet (* or *) Times@@@Select[Subsets[Prime[ Range[ 300]],{2}],#[[2]]-#[[1]]==Total[IntegerDigits[#[[1]]#[[2]]]]&] (* _Harvey P. Dale_, Oct 14 2021 *)
%o A308821 (PARI) isok(n) = (bigomega(n) == 2) && (f=factor(n)) && (#f~ == 2) && (sumdigits(n) == f[2,1] - f[1,1]); \\ _Michel Marcus_, Jun 29 2019
%o A308821 (Magma) [n:n in [2..2100000]|IsSquarefree(n) and #PrimeDivisors(n) eq 2 and PrimeDivisors(n)[2]-PrimeDivisors(n)[1] eq &+Intseq(n)]; // _Marius A. Burtea_, Jul 27 2019
%Y A308821 Cf. A001358, A006753, A006881.
%K A308821 nonn,base
%O A308821 1,1
%A A308821 _James Beyer_, Jun 26 2019