A071583 -id:A071583 - cp's OEIS frontend

A058993 Numbers m such that 5^m reversed is a prime.

1, 3, 26, 36, 43, 66, 76, 149, 511, 885, 3767, 18157, 20516, 26316

Offset: 1

Robert G. Wilson v, Jan 17 2001

Numbers m such that k^m reversed is prime: A057708 (k=2), A350441 (k=4), this sequence (k=5), A058994 (k=7), A350442 (k=8), A058995 (k=13).

Do[ If[ PrimeQ[ ToExpression[ StringReverse[ ToString[5^n] ] ] ], Print[n] ], {n, 1, 3000} ]

isok(m) = isprime(fromdigits(Vecrev(digits(5^m)))) \\ Mohammed Yaseen, Jul 20 2022

from sympy import isprime
k, m, A058993_list = 1, 5,  []
while k <= 10**3:
    if isprime(int(str(m)[::-1])):
        A058993_list.append(k)
    k += 1
    m *= 5 # Chai Wah Wu, Mar 09 2021

a(12)-a(14) from Michael S. Branicky, Apr 01 2023

A158624 Upper limit of backward value of 5^n.

Original entry on oeis.org

5, 2, 6, 5, 6, 7, 9, 5, 7, 8, 7, 9, 6, 9, 9, 7, 6, 5, 7, 8, 8, 5, 5, 7, 6, 9, 7, 5, 9, 9, 5, 7, 8, 9, 5, 8, 6, 7, 7, 5, 6, 5, 6, 9, 5, 7, 5, 6, 6, 9, 6, 7, 7, 6, 7, 6, 8, 8, 5, 8, 5, 6, 7, 5, 8, 9, 6, 6, 7, 5, 9, 5, 7, 9, 8, 6, 8, 8, 7, 9, 5, 8, 8, 5, 8, 5, 9, 5, 5, 8, 9, 7, 7, 9, 7, 7, 9, 6, 7, 6, 8, 9, 7, 6, 6

Offset: 0

Simon Plouffe, Mar 23 2009

Digits are all in {5,6,7,8,9} after 2nd term.
The other limit, related to odd n, is in A158625.
The first digit of the backward value of 5^n is always a(0)=5. The second digit is a(-1)=2 from n=2 on. The third digit is a(-2)=6 for all even n >= 4. The fourth digit is a(-3)=5 for n=6+4k, k >= 0. The fifth digit is a(-4)=6 for n=10+8k, k >= 0. The 6th digit is a(-5)=7 for n=10+16k, k >= 0. The 7th digit is a(-6)=9 for n=10+32k, k >= 0.

			5^3 = 125 so the backward value is 0.521, 5^10 = 9765625, so the backward value is 0.5265679. The upper limit of all values is a constant, which appears to be 0.5265679578796997657885576975995789586775656...

Robert Israel, Table of n, a(n) for n = 0..999

Cf. A158625, A071583, A145679.

D:=87; e:=6; for d in [2..D-1] do t:=Modexp(5, e, 10^(d+1)); if t div 10^d lt 5 then e+:=2^(d-2); end if; end for; t:=Modexp(5, e, 10^D); IntegerToSequence(t, 10); // Jon E. Schoenfield, Feb 07 2018

A158624:= proc(N)
local m,n,A;
m[2]:= 3;
for n from 3 to N do
  A:= 5&^m[n-1] mod 10^n;
  if A > 5*10^(n-1) then m[n]:= m[n-1]
  else m[n]:= m[n-1]+2^(n-3)
  end if
end do:
convert(5&^m[N] mod 10^(N),base,10);
end proc; # Robert Israel, Apr 01 2012

A158624[k_] := Module[{m, n, a}, m[2] = 3; For[n = 3, n <= k, n++, a = PowerMod[5, m[n-1], 10^n]; If[ a > 5*10^(n-1), m[n] = m[n-1], m[n] = m[n-1] + 2^(n-3)]]; IntegerDigits[PowerMod[5, m[k], 10^k]] // Reverse]; A158624[105] (* Jean-François Alcover, Dec 21 2012, translated from Robert Israel's Maple program *)

A071586 Powers of 8 written backwards.

Original entry on oeis.org

1, 8, 46, 215, 6904, 86723, 441262, 2517902, 61277761, 827712431, 4281473701, 2954399858, 63767491786, 888318557945, 4011156408934, 23888027348153, 656017679474182, 8425863189971522, 48918490589341081, 278558570881511441

Offset: 0

Benoit Cloitre, Jun 01 2002

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A004094, A004167, A071582, A071583, A071588, A071584, A071587.

for(i=1,50,n=8^i; s=ceil(log(n)/log(10)); print1(sum(i=0,s,10^(s-i-1)*(floor(n/10^i)-10*floor(n/10^(i+1)))),","))

A071588 Powers of 6 written backwards.

Original entry on oeis.org

1, 6, 63, 612, 6921, 6777, 65664, 639972, 6169761, 69677001, 67166406, 650797263, 6332876712, 61049606031, 69046146387, 675489481074, 6547099011282, 63744495662961, 614866659955101, 694010047953906, 6792600448516563

Offset: 0

Benoit Cloitre, Jun 01 2002

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A000400, A004086, A004094, A004167, A071582, A071583, A071584, A071586, A071587.

FromDigits[Reverse[IntegerDigits[#]]]&/@(6^Range[0,30]) (* Harvey P. Dale, Feb 02 2012 *)

for(i=1,50,n=5^i; s=ceil(log(n)/log(10)); print1(sum(i=0,s,10^(s-i-1)*(floor(n/10^i)-10*floor(n/10^(i+1)))),","))

a(n) = A004086(A000400(n)).

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A058993 Numbers m such that 5^m reversed is a prime.

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A158624 Upper limit of backward value of 5^n.

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A071586 Powers of 8 written backwards.

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A071588 Powers of 6 written backwards.

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