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A109133 Numbers k such that (sum of digits)*(number of digits) + 1 is prime. 1
1, 2, 4, 6, 10, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 41, 42, 44, 45, 47, 50, 51, 53, 54, 56, 59, 60, 62, 63, 65, 68, 69, 71, 72, 74, 77, 78, 80, 81, 83, 86, 87, 90, 92, 95, 96, 99, 101, 103, 105, 109, 110, 112, 114, 118, 121, 123, 127 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
By Dirichlet's theorem on primes in arithmetic progressions, for any positive integer k this sequence has infinitely many terms of the form k*10^m. - Robert Israel, Dec 19 2021
LINKS
EXAMPLE
1234 is a term because 4*(1+2+3+4)+1 = 41.
MAPLE
filter:= proc(n) local L;
L:= convert(n, base, 10);
isprime(convert(L, `+`)*nops(L)+1)
end proc:
select(filter, [$1..200]); # Robert Israel, Dec 19 2021
MATHEMATICA
Select[Range[130], PrimeQ[Total[IntegerDigits[#]]IntegerLength[ #]+ 1]&] (* Harvey P. Dale, Jul 12 2011 *)
PROG
(Python)
from sympy import isprime
def ok(n): s = str(n); return isprime(sum(map(int, s))*len(s) + 1)
print([k for k in range(128) if ok(k)]) # Michael S. Branicky, Dec 19 2021
CROSSREFS
Cf. A110805.
Sequence in context: A089227 A204660 A275956 * A056077 A249428 A129630
KEYWORD
base,easy,nonn
AUTHOR
Jason Earls, Aug 17 2005
STATUS
approved

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Last modified July 14 11:30 EDT 2024. Contains 374318 sequences. (Running on oeis4.)