A097385 -id:A097385 - cp's OEIS frontend

A097387 Let f(x)=(largest digit of x)^(smallest digit of x) + x (A097385). Sequence gives numbers n such that f(n) and f(n+1) are both prime.

60, 460, 640, 820, 1360, 1480, 1620, 1870, 2110, 2380, 3460, 3630, 3880, 4560, 4650, 5640, 5650, 5860, 6210, 6310, 6360, 6420, 7480, 8170, 8680, 8830, 11680, 11830, 12280, 12640, 12820, 13780, 14620, 15460, 15640, 15660, 15880, 16410, 16420

Offset: 1

Jason Earls, Aug 18 2004

Conjecture: Terms will always be multiples of ten. Aug 21, 2004: Dean Hickerson proved this.

			640 is in the sequence because 6^0 + 640 = 641 and 6^1 + 641 = 647, both prime.

Cf. A054054, A054055, A097385, A097386.

A097386 Numbers n such that (largest digit of n)^(smallest digit of n) + n is prime.

Original entry on oeis.org

1, 10, 21, 30, 32, 40, 43, 60, 61, 65, 70, 81, 92, 100, 102, 106, 108, 130, 150, 152, 161, 172, 174, 180, 183, 185, 190, 210, 221, 232, 240, 250, 252, 270, 280, 283, 285, 292, 298, 306, 310, 322, 330, 354, 361, 372, 376, 381, 394, 400, 408, 420, 423, 430, 460

Offset: 1

Jason Earls, Aug 18 2004

No term ends in 9. Conjecture: Let f(x)=(largest digit of x)^(smallest digit of x) + x. There are infinitely many positive integers n such that f(n) and f(n+1) are both prime; see A097387.

			1272 is in the sequence because 7^2 + 1272 = 1321, a prime.

Cf. A054054, A054055, A097385, A097387.

okQ[n_]:=Module[{idn=IntegerDigits[n]},PrimeQ[Max[idn]^Min[idn]+n]]
Select[Range[500],okQ] (* Harvey P. Dale, Dec 11 2010 *)

Corrected by T. D. Noe, Oct 25 2006

A386253 a(n) = (smallest digit of n)^(largest digit of n) + n.

Original entry on oeis.org

1, 2, 6, 30, 260, 3130, 46662, 823550, 16777224, 387420498, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 22, 26, 31, 40, 57, 90, 155, 284, 541, 30, 32, 40, 60, 115, 278, 765, 2224, 6599, 19722, 40, 42, 58, 124, 300, 1069, 4142, 16431, 65584, 262193, 50

Offset: 0

Mia Boudreau, Jul 16 2025

0^0 is an indeterminate form, but for the purpose of a(0) it is taken to be 1. - Robert Israel, Jul 22 2025

			a(563) = 1292 because 3^6 + 563 = 1292.

Mia Boudreau, Table of n, a(n) for n = 0..10000

Cf. A054054, A054055, A097385.

f:= proc(n) local L; L:= convert(n,base,10); n + min(L)^max(L) end proc:
map(f, [$0..100]); # Robert Israel, Jul 22 2025

Unprotect[Power]; 0^0:=1; Protect[Power]; a[n_]:= (Min[IntegerDigits[n]])^(Max[IntegerDigits[n]]) + n; Array[a,51,0] (* Stefano Spezia, Jul 17 2025 *)

def a(n): return int(min(s:=str(n)))**int(max(s)) + n
print([a(n) for n in range(51)]) # Michael S. Branicky, Jul 21 2025

a(n) = A054054(n)^A054055(n) + n.

cp's OEIS Frontend

A097387 Let f(x)=(largest digit of x)^(smallest digit of x) + x (A097385). Sequence gives numbers n such that f(n) and f(n+1) are both prime.

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A097386 Numbers n such that (largest digit of n)^(smallest digit of n) + n is prime.

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A386253 a(n) = (smallest digit of n)^(largest digit of n) + n.

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