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A290450
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Primes with property that the next prime has the same last digit.
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5
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139, 181, 241, 283, 337, 409, 421, 547, 577, 631, 691, 709, 787, 811, 829, 887, 919, 1021, 1039, 1051, 1153, 1171, 1249, 1399, 1471, 1627, 1637, 1699, 1723, 1801, 1879, 2017, 2029, 2053, 2089, 2143, 2521, 2647, 2719, 2731, 2767, 2887, 2917, 3001, 3089, 3109, 3361, 3413, 3517, 3547, 3571
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OFFSET
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1,1
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COMMENTS
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Starts off the same as A031928, primes p such that the next prime is p + 10. First term that differs is 887, since 897 = 3 * 13 * 23 and the next prime is 907.
As the primes get larger and more sparsely distributed, the difference between successive primes is less likely to be less than 10.
One might expect that a prime is 1/4 as likely to be followed by a prime with the same least significant digit in base 10 (since the possibilities are 1, 3, 7, 9).
One might also expect this sequence to consist of a quarter of the primes. And yet pi(a(50)) = pi(3547) = 497; the 200th prime is 1223.
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LINKS
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FORMULA
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EXAMPLE
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139 is in the sequence because the immediately following prime is 149, which also ends in 9.
But 149 is not in the sequence because the next prime after that one is 151, which ends in 1, not 9.
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MATHEMATICA
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Select[Partition[Prime[Range[500000]], 2, 1], Mod[#[[1]], 10] == Mod[#[[2]], 10] &][[All, 1]] ( * Harvey P. Dale, Aug 21 2017 *)
Module[{nn=500000, prs, p}, prs=Prime[Range[nn]]; p=Divisible[#, 10]&/@ Differences[prs]; Pick[Most[prs], p]] (* Harvey P. Dale, Aug 22 2017 *)
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PROG
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(Magma) f:=func<p, m|p mod 10 eq m and NextPrime(p) mod 10 eq m>; a:=[]; for p in PrimesUpTo(4000) do if f(p, 1) or f(p, 3) or f(p, 7) or f(p, 9) then Append(~a, p); end if; end for; a; // Marius A. Burtea, Oct 16 2019
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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