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 A210513 Primes formed by concatenating k, k, and 7. 2
 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, 103110317, 103410347, 103810387 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is similar to A030458, A052089, and A092994. Base considered is 10. Observations: - k cannot be a multiple of 7. - k cannot have a digital root 7 as the sum of the digits would be divisible by 3. - There is no k between 100 and 1000 that can form a prime number of this form after 95957 the next prime is 101710177. - k 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 Michael S. Branicky, Table of n, a(n) for n = 1..10000 EXAMPLE For k = 2, a(1) = 227. For k = 3, a(2) = 337. For k = 5, a(3) = 557. For k = 8, a(4) = 887. For k = 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 from functools import reduce 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, end=', ') (Python) from sympy import isprime from itertools import count, islice def agen(): yield from filter(isprime, (int(str(k)+str(k)+'7') for k in count(1))) print(list(islice(agen(), 36))) # Michael S. Branicky, Jul 26 2022 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 EXTENSIONS a(34) and beyond from Michael S. Branicky, Jul 26 2022 STATUS approved

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Last modified February 25 11:11 EST 2024. Contains 370324 sequences. (Running on oeis4.)