A303918 Prime numbers with property that left half and right half have the same pattern of consecutive increasing/decreasing/equal digits:.

1021, 1031, 1051, 1061, 1063, 1087, 1091, 1093, 1097, 1201, 1213, 1217, 1223, 1229, 1237, 1249, 1259, 1279, 1289, 1301, 1303, 1307, 1319, 1327, 1367, 1409, 1423, 1427, 1429, 1439, 1447, 1459, 1489, 1523, 1549, 1559, 1567, 1579, 1601, 1607, 1609, 1613, 1619, 1627, 1637, 1657, 1667, 1669, 1709, 1723, 1747

Offset

1,1

Comments

Each term in the sequence must have an even number of digits to allow comparison of its two halves. Minimum four-digit term is 1021, maximum is 9887; minimum six-digit term is 100411, maximum is 998551.

Links

Table of n, a(n) for n=1..51.

Example

1021 belongs to the sequence as it is prime and the consecutive digits in its left and right halves (10 and 21, respectively) have the same pattern: 1 > 0, 2 > 1.
The prime number 100411 belongs to the sequence as the consecutive digits in its left half (100) and right half (411) have the same pattern: 1 > 0 = 0, 4 > 1 = 1.

Mathematica

pt[w_] := Sign@ Differences@ w; ok[p_] := PrimeQ[p] && Block[{d = IntegerDigits[p], m}, m = Length[d]; EvenQ[m] && pt@ Take[d, m/2] == pt@ Take[d, -m/2]]; Select[ Range[1000, 1747], ok] (* Giovanni Resta, May 04 2018 *)

Prog

(Python)
#program to get all terms less than one million
def pattern(p):
    l=len(p)
    s=""
    for k in range(l-1):
        if p[k+1]>p[k]: s=s+"+"
        elif p[k+1]<p[k]: s=s+"-"
        else: s=s+"="
    return(s)
def is_prime(num):
    for k in range(2, num):
       if (num % k) == 0:
           return(0)
    return(1)
for i in range(1000, 999999):
    if len(str(i)) % 2 == 0:
        p1=str(i)[0:int(len(str(i))/2)]
        p2=str(i)[int(len(str(i))/2):len(str(i))]
        if pattern(p1)==pattern(p2) and is_prime(i):  print(i)

Crossrefs

Cf. A000040.

Sequence in context: A024020 A069791 A167846 * A371378 A228625 A356947

Adjacent sequences: A303915 A303916 A303917 * A303919 A303920 A303921

Keyword

nonn,base

Author

Pierandrea Formusa, May 02 2018

Status

approved