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A346206 Primes p, with k digits, such that the Sum_{i=1..k} (p without its i-th digit)/(its i-th digit) is a prime. 2
11, 21673, 27367, 32611, 33311, 41141, 48821, 82781, 171263, 211441, 243433, 323443, 343243, 449699, 632623, 663661, 727271, 772127, 847871, 882881, 944969, 1129699, 1192699, 1193939, 1262633, 1334341, 1342433, 1343423, 1361441, 1388641, 1399193, 1461883, 1613441 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Michel Marcus, Table of n, a(n) for n = 1..441

Carlos Rivera, Puzzle 1045. One nice puzzle from Paolo Lava, The Prime Puzzles and Problems Connection.

EXAMPLE

21673 gives 1673/2 + 2673/1 + 2173/6 + 2163/7 + 2167/3 = 4903; so 21673 is a term.

PROG

(PARI) subs(d, j) = {my(x=""); for (k=1, #d, if (j != k, x = concat(x, d[k])); ); eval(x); }

isok(p) = {my(d=digits(p), res);  if (isprime(p) && vecmin(d), res = sum(j=1, #d, subs(d, j)/d[j]); (denominator(res)==1) && isprime(res); ); }

(Python)

from sympy import isprime, primerange

from fractions import Fraction

def ok(p):

    s = str(p)

    if '0' in s or len(s) == 1: return False

    f = sum(Fraction(int(s[:i]+s[i+1:]), int(s[i])) for i in range(len(s)))

    return f.denominator == 1 and isprime(f.numerator)

def aupto(lim): return [p for p in primerange(1, lim+1) if ok(p)]

print(aupto(1620000)) # Michael S. Branicky, Jul 11 2021

CROSSREFS

Subsequence of A038618 (zeroless primes).

Sequence in context: A330301 A264917 A198668 * A198707 A198626 A343119

Adjacent sequences:  A346203 A346204 A346205 * A346207 A346208 A346209

KEYWORD

nonn,base

AUTHOR

Michel Marcus, Jul 10 2021

STATUS

approved

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Last modified September 30 02:38 EDT 2022. Contains 357095 sequences. (Running on oeis4.)