A163622 Composite numbers such that the sum of its smallest digit and the largest digit is a prime.

12, 14, 16, 20, 21, 25, 30, 32, 34, 38, 49, 50, 52, 56, 58, 65, 70, 74, 76, 85, 92, 94, 98, 102, 105, 112, 114, 116, 120, 121, 122, 124, 126, 130, 134, 136, 141, 142, 143, 144, 146, 150, 156, 161, 162, 164, 165, 166, 170, 200, 201, 202, 203, 205, 207, 210

Offset

1,1

Comments

Numbers like 111 are ignored, at least two different digits are required.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Example

166 is a composite number whose sum of smallest digit and the largest digit is a prime.

Mathematica

comprQ[n_]:=Module[{idn=IntegerDigits[n]}, CompositeQ[n]&&Length[Union[ idn]]>1&&PrimeQ[Min[idn]+Max[idn]]]; Select[Range[250], comprQ] (* Harvey P. Dale, Mar 29 2015 *)

Prog

(Python)
from sympy import isprime
def ok(n):
    digits = list(map(int, str(n)))
    repdigit, smlg = len(set(digits)) == 1, min(digits) + max(digits)
    return not repdigit and isprime(smlg) and not isprime(n)
print([k for k in range(211) if ok(k)]) # Michael S. Branicky, Dec 14 2021

Crossrefs

Cf. A002808, A162658, A141642, A221699.

Sequence in context: A135739 A096923 A141642 * A159251 A208156 A135770

Adjacent sequences: A163619 A163620 A163621 * A163623 A163624 A163625

Keyword

nonn,base

Author

Parthasarathy Nambi, Aug 01 2009

Extensions

Corrected and extended by Harvey P. Dale, Mar 29 2015

Status

approved