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

14, 95, 527, 851, 1247, 3551, 4307, 8051, 14351, 26969, 30227, 37769, 64769, 87953, 152051, 163769, 199553, 202451, 256793, 275369, 341969, 455369, 1070969, 1095953, 1159673, 1232051, 1625369, 1702769, 2005007, 2081993

Offset

1,1

Comments

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.

Links

James Beyer, Table of n, a(n) for n = 1..1000

James Beyer, Numbers Like Fourteen

Wikipedia, Digit sum

Wikipedia, Semiprime

Example

14=2*7 and 1+4=7-2.
95=5*19 and 9+5=19-5.
527=17*31 and 5+2+7=31-17.

Mathematica

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 *)
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 *)

Prog

(PARI) isok(n) = (bigomega(n) == 2) && (f=factor(n)) && (#f~ == 2) && (sumdigits(n) == f[2, 1] - f[1, 1]); \\ Michel Marcus, Jun 29 2019
(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

Crossrefs

Cf. A001358, A006753, A006881.

Sequence in context: A044646 A241205 A055844 * A274724 A254469 A372661

Adjacent sequences: A308818 A308819 A308820 * A308822 A308823 A308824

Keyword

nonn,base

Author

James Beyer, Jun 26 2019

Status

approved