cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A097223 Prime numbers p such that p = prime(n) and n = product of the digits of p.

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%I A097223 #22 Jun 14 2025 00:29:56
%S A097223 17,73,2475989
%N A097223 Prime numbers p such that p = prime(n) and n = product of the digits of p.
%C A097223 This sequence is a subsequence of A097220, so the sequence is also a subsequence of A097221.
%C A097223 There is no further term. - _Farideh Firoozbakht_, Jul 15 2009
%H A097223 Jessie Byrnes, Chris Spicer and Alyssa Turnquist, <a href="https://doi.org/10.4169/mathhorizons.23.2.12">The Sheldon Conjecture</a>. Math Horizons, Vol. 23, No. 2 (November 2015), pp. 12-15 (4 pages); <a href="https://www.jstor.org/stable/10.4169/mathhorizons.23.2.12">alternate link</a>.
%H A097223 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=2475989">2475989</a>
%H A097223 Carl Pomerance, <a href="https://www.math.dartmouth.edu/~carlp/illinoistalk1.pdf">What we still don't know about addition and multiplication</a>, Trjitzinsky Lecture 1, U. Illinois Urbana-Champaign, November 27, 2018. See slides 22 & 24.
%H A097223 Carl Pomerance and Chris Spicer, <a href="https://doi.org/10.1080/00029890.2019.1626672">Proof of the Sheldon Conjecture</a>, The American Mathematical Monthly, September 2019, 126(8), 688-698; <a href="https://math.dartmouth.edu/~carlp/sheldon02132019.pdf">alternate link</a>.
%e A097223 2475989 is in the sequence because 2475989 is (2*4*7*5*9*8*9)-th prime.
%t A097223 v={}; Do[If[h=IntegerDigits[Prime[n]]; l=Length[h]; p=Product[h[[k]], {k, l}]; p==n, v=Append[v, Prime[n]]; Print[v]], {n, 205000000}]
%o A097223 (PARI) isok(p) = isprime(p) && (primepi(p) == vecprod(digits(p))); \\ _Michel Marcus_, Jan 27 2019
%Y A097223 Cf. A097220, A097221.
%K A097223 base,fini,full,nonn,bref
%O A097223 1,1
%A A097223 _Farideh Firoozbakht_, Aug 06 2004