A384954 Primes such that moving the last digit to the front produces a triangular number.

3, 19, 2251, 3169, 6553, 7309, 7507, 13789, 20107, 21313, 38611, 39619, 43651, 44533, 48781, 52453, 54001, 54667, 65809, 70201, 75781, 76753, 78157, 79039, 87211, 173359, 188281, 196003, 247501, 366103, 370261, 390763, 435907, 482401, 498781, 540613, 542719

Offset

1,1

Comments

Leading zeros are not allowed.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..22806

Example

2251 is a prime number and 1225 is a triangular number, so 2251 is a term.

Maple

q:= proc(n) n=3 or isprime(n) and issqr(1+8*parse(cat(irem(n, 10, 'm'), m))) end:
select(q, [$2..650000])[];  # Alois P. Heinz, Jun 14 2025

Mathematica

Select[Prime[Range[45000]], OddQ[Sqrt[8*FromDigits[RotateRight[IntegerDigits[#]]]+1]]&] (* Harvey P. Dale, Aug 01 2025 *)

Prog

(Python)
from itertools import accumulate, count
from sympy import isprime
def rotate_left(n): return (s := str(n))[1:] + s[0]
def a384954_gen(lim): # Must be a power of 10. Terms are not generated in order.
    for triangle in accumulate(count()):
        if triangle >= lim: break
        rotated = rotate_left(triangle)
        if rotated[0] != '0' and isprime(p := int(rotated)):
            yield p
print(sorted(a384954_gen(10**6))) # David Radcliffe, Jun 13 2025

Crossrefs

Cf. A000040, A000217, A133197.

Sequence in context: A098796 A365579 A120563 * A182344 A191623 A164063

Adjacent sequences: A384951 A384952 A384953 * A384955 A384956 A384957

Keyword

nonn,base

Author

David Radcliffe, Jun 13 2025

Status

approved