A112375 Concatenation of base and exponent of prime powers.

21, 31, 22, 51, 71, 23, 32, 111, 131, 24, 171, 191, 231, 52, 33, 291, 311, 25, 371, 411, 431, 471, 72, 531, 591, 611, 26, 671, 711, 731, 791, 34, 831, 891, 971, 1011, 1031, 1071, 1091, 1131, 112, 53, 1271, 27, 1311, 1371, 1391, 1491, 1511, 1571, 1631, 1671

Offset: 1

Author

Zak Seidov, Dec 04 2005

Keywords

• nonn
• base

Comments

If n = p^q, where p is prime and q > 0, then p concatenated with q is in the sequence.

Might be a good "puzzle" sequence - guess the rule given the first ten or so terms.

Examples

			n = 3 = 3^1, so (3 concatenated with 1) = 31 is a term.
		

Links

• Robert Price, Table of n, a(n) for n = 1..1280

Crossrefs

Cf. A112376, A064438, A067599.

Programs

Mathematica

Map[FromDigits, Select[Table[FactorInteger[i], {i, 2, 10000}],
Length[#] == 1 &], 2] (* Robert Price, Mar 15 2020 *)

PARI

for(n=1,300,fac=factor(n);if(matsize(fac)[1]==1,print1(eval(concat(Str(fac[1,1]),Str(fac[1,2]))),",")))

Formula

a(n) = A067599(A246655(n)) = A067599(A000961(n+1)). - M. F. Hasler, Mar 14 2018

Extensions

Edited and extended by Klaus Brockhaus, Jan 21 2006