

A303918


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


0



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
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OFFSET

1,1


COMMENTS

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


LINKS



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(l1):
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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



