A045336 Palindromic terms from A019546.

2, 3, 5, 7, 353, 373, 727, 757, 32323, 33533, 35353, 35753, 37273, 37573, 72227, 72727, 73237, 75557, 77377, 3222223, 3223223, 3233323, 3252523, 3272723, 3337333, 3353533, 3553553, 3722273, 3732373, 3773773, 7257527, 7327237, 7352537, 7527257, 7722277

Offset

1,1

Comments

a(33) = 7352537 is the smallest palindromic prime using all prime digits (see Prime Curios! link). - Bernard Schott, Nov 10 2020

Links

Michael S. Branicky, Table of n, a(n) for n = 1..12725 (all terms with <= 17 digits; terms 1..330 from Harvey P. Dale)

Chris K. Caldwell and G. L. Honaker, Jr., 7352537, Prime Curios!

Mathematica

Select[ Range[ 1, 10^7 ], PrimeQ[ # ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 0 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 1 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 4 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 6 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 8 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 9 ] && RealDigits[ # ][ [ 1 ] ] == Reverse[ RealDigits[ # ][ [ 1 ] ] ] & ]
Table[FromDigits/@Select[Tuples[{2, 3, 5, 7}, n], #==Reverse[#]&&PrimeQ[ FromDigits[ #]]&], {n, 12}]//Flatten (* Harvey P. Dale, Jun 19 2016 *)
f@n_ := Prime@n;
g@l_ := FromDigits@# & /@ Table[Join[l, {f@i}, Reverse@l], {i, 4}];
Flatten[g@# & /@ (f@# & /@
     Select[Table[IntegerDigits[n, 5], {n, 2000}], FreeQ[#, 0] &])] //
Select[PrimeQ] (* Hans Rudolf Widmer, Dec 18 2021 *)

Prog

(Python)
from sympy import isprime
from itertools import count, product, takewhile
def primedigpals():
    for d in count(1, 2):
        for p in product("2357", repeat=d//2):
            left = "".join(p)
            for mid in "2357":
                yield int(left + mid + left[::-1])
def aupto(N):
    return list(takewhile(lambda x: x<=N, filter(isprime, primedigpals())))
print(aupto(10**7)) # Michael S. Branicky, Dec 18 2021

Crossrefs

Cf. A019546 and A002385.

Sequence in context: A052023 A052025 A359491 * A083183 A046477 A360789

Adjacent sequences: A045333 A045334 A045335 * A045337 A045338 A045339

Keyword

nonn,base

Author

Robert G. Wilson v, Aug 18 2000

Status

approved