A382765 Primes that can be expressed using exactly one of each of the prime digits 2, 3, 5, 7, using concatenation and the arithmetic operations +,-,*,/,^.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 103, 107, 113, 139, 149, 151, 163, 167, 173, 181, 197, 211, 223, 227, 229, 257, 263, 311, 353, 359, 367, 373, 379, 389, 479, 569, 571, 643, 691, 727, 733, 751, 877, 1019, 1091, 1699, 2239, 2357, 2749, 2753

Offset

1,1

Comments

Concatenation is only allowed for individual digits, not expressions, so 37 - 2^5 = 5 is allowed but (7 + 2 - 5)3 = 43 is not allowed.

Links

Robert Israel, Table of n, a(n) for n = 1..83 (full sequence)

Robert Israel, Maple code

Robert Israel, An expression for each term

Example

a(1) = 2 = (3 - 2) * (7 - 5).
a(2) = 3 = 2 + 3 + 5 - 7.
a(3) = 5 = 37 - 2^5.
a(4) = 7 = 2 + 3 - 5 + 7.
a(83) = 4747561509941 = 7 ^ (3 * 5) - 2.

Maple

See link.

Crossrefs

Cf. A382901.

Sequence in context: A069684 A061022 A238852 * A079152 A124590 A049573

Adjacent sequences: A382762 A382763 A382764 * A382766 A382767 A382768

Keyword

nonn,base,fini,full

Author

Zak Seidov and Robert Israel, Apr 10 2025

Status

approved