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

1,1

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.

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A112376, A064438, A067599.

Sequence in context: A116096 A116116 A079394 * A067599 A342838 A261322

Adjacent sequences: A112372 A112373 A112374 * A112376 A112377 A112378

Keyword

nonn,base

Author

Zak Seidov, Dec 04 2005

Extensions

Edited and extended by Klaus Brockhaus, Jan 21 2006

Status

approved