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A231588
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Primes with decimal digits in arithmetic progression mod 10.
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3
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 109, 173, 197, 307, 383, 593, 727, 739, 937, 2963, 4567, 4703, 5791, 7159, 8147, 9371, 10987, 15937, 19753, 37159, 52963, 53197, 58147, 71593, 72727, 73951, 76543
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listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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This sequence contains straight-line primes (A167847).
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LINKS
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EXAMPLE
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(7,2,7,2,7,...) is an arithmetic progression mod 10, hence the prime number 72727 appears in this sequence.
(7,6,5,4,3,...) is an arithmetic progression mod 10, hence the prime number 76543 appears in this sequence.
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MATHEMATICA
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Select[Prime[Range[PrimePi[76543]]], Length[Union[Mod[Differences[IntegerDigits[#]], 10]]] <= 1 &]
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PROG
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(PARI) See Link section.
(Python)
from sympy import isprime
from itertools import count, islice
def bgen():
yield from [2, 3, 5, 7]
yield from (int("".join(str((s0+i*r)%10) for i in range(d))) for d in count(2) for s0 in range(1, 10) for r in range(-s0, 10-s0))
def agen(): yield from filter(isprime, bgen())
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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