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A210513 Primes formed by concatenating N, N, and 7. 1
227, 337, 557, 887, 997, 11117, 24247, 26267, 27277, 29297, 30307, 32327, 39397, 48487, 51517, 54547, 60607, 62627, 65657, 68687, 69697, 72727, 74747, 78787, 81817, 87877, 89897, 90907, 92927, 93937, 95957, 101710177, 101910197 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This series is similar to A030458 and A052089

Base considered is 10

Observation:

- N cannot be a multiple of 7

- N cannot have a digital root 7 as the sum of the digits would be divisible by 3

- This series is similar to A092994

- There is no N between 100 and 1000 that can form a prime number of this form after 95957 the next prime is 101710177

- N cannot have a digital root equal to 1 or 4, because then in the concatenation it contributes 2 or 8 to the digital root of the number, and that number is then divisible by 3.

LINKS

Table of n, a(n) for n=1..33.

EXAMPLE

for n = 2, a(1) = 227.

for n = 3, a(2) = 337.

for n = 5, a(3) = 557.

for n = 8, a(4) = 887.

for n = 9, a(5) = 997.

MATHEMATICA

Select[Table[FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[n], {7}}]], {n, 100}], PrimeQ] (* Alonso del Arte, Feb 01 2013 *)

PROG

(Python)

import numpy as np

def factors(n):

....return reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))

for i in range(1, 2000):

....p1=int(str(i)+str(i)+"7")

....if len(factors(p1))<3:

........print p1

CROSSREFS

Cf. A030458, A052089, A092994.

Sequence in context: A142261 A117458 A252026 * A142842 A142545 A088788

Adjacent sequences:  A210510 A210511 A210512 * A210514 A210515 A210516

KEYWORD

base,nonn,easy

AUTHOR

Abhiram R Devesh, Jan 26 2013

STATUS

approved

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Last modified December 17 03:19 EST 2018. Contains 318192 sequences. (Running on oeis4.)