A069707 -id:A069707 - cp's OEIS frontend

A069706 Primes with property that swapping first and last digits also gives a prime.

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 101, 107, 113, 131, 149, 151, 157, 167, 179, 181, 191, 199, 311, 313, 337, 347, 353, 359, 373, 383, 389, 701, 709, 727, 733, 739, 743, 751, 757, 761, 769, 787, 797, 907, 919, 929, 937, 941, 953, 967, 971, 983, 991, 1009, 1013

Offset: 1

Amarnath Murthy, Apr 08 2002

This is not the same as A007500, "palindromic" primes.

			1049 and 9041 both are primes hence both are members.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A007500, A069707, A069708.

swapdigs:= proc(n) local d;
  d:= ilog10(n);
  n + ((n mod 10)-floor(n/10^d))*(10^d-1);
end proc:
select(isprime and isprime @ swapdigs, [2,seq(2*i+1,i=1..10^4)]); # Robert Israel, Nov 11 2015

Do[t = IntegerDigits[ Prime[n]]; u = t; u[[1]] = t[[ -1]]; u[[ -1]] = t[[1]]; t = FromDigits[u]; If[ PrimeQ[t], Print[ Prime[n]]], {n, 1, 300}]

from sympy import prime, isprime
A069706_list = [2,3,5,7]
for i in range(5,10**6):
    p = prime(i)
    s = str(p)
    if isprime(int(s[-1]+s[1:-1]+s[0])):
        A069706_list.append(p) # Chai Wah Wu, Nov 11 2015

Edited and extended by Robert G. Wilson v, Apr 12 2002

Edited by N. J. A. Sloane, Jan 20 2009

A069708 Triangular numbers with property that swapping first and last digits also gives a triangular number.

Original entry on oeis.org

1, 3, 6, 10, 55, 66, 120, 153, 171, 190, 300, 351, 595, 630, 666, 820, 1081, 1431, 1711, 1891, 3003, 3403, 5050, 5460, 5565, 5995, 6216, 6786, 8128, 8778, 10011, 10731, 11781, 12561, 13041, 13861, 15051, 15931, 16471, 17020, 17391, 17578, 18721

Offset: 1

Amarnath Murthy, Apr 08 2002

934 of the first 1000 terms begin and end with the same digit. 40 of the first 1000 terms end in zero. Thus, only 26 of the first 1000 terms begin and end with different nonzero digits, with 153 being the smallest and 8026021 being the largest of those terms. - Harvey P. Dale, Jan 09 2021

			820 and 028 = 28 both are triangular numbers hence both are members.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A069706, A069707.

Do[t = IntegerDigits[n(n + 1)/2]; u = t; u[[1]] = t[[ -1]]; u[[ -1]] = t[[1]]; t = FromDigits[u]; u = Floor[ Sqrt[2t]]; If[ u(u + 1)/2 == t, Print[n(n + 1)/2]], {n, 1, 300}]
sfl[n_]:=Module[{idn=IntegerDigits[n]},FromDigits[Flatten[Join[{Last[ idn],Rest[ Most[ idn]],First[ idn]}]]]]; Join[ {1,3,6},Select[ Accumulate[ Range[200]],OddQ[Sqrt[8 sfl[#]+1]]&]//Quiet] (* Harvey P. Dale, Jan 09 2021 *)

Edited, corrected and extended by Robert G. Wilson v

Edited by N. J. A. Sloane, Jan 20 2009

cp's OEIS Frontend

A069706 Primes with property that swapping first and last digits also gives a prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Python

Extensions