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A353136
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Primes whose gaps to both neighbor primes are triangular numbers.
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5
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53, 157, 173, 251, 257, 263, 337, 373, 547, 557, 563, 577, 587, 593, 607, 653, 733, 947, 977, 1039, 1103, 1123, 1181, 1187, 1223, 1367, 1627, 1747, 1753, 1907, 2017, 2063, 2287, 2417, 2677, 2719, 2897, 2903, 2963, 3307, 3313, 3517, 3547, 3637, 3733, 4013, 4211
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OFFSET
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1,1
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..10000
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EXAMPLE
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Prime 251 is a term, the gap to the previous prime 241 is 10 and the gap to the next prime 257 is 6 and both gaps are triangular numbers.
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MAPLE
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t:= proc(n) option remember; issqr(8*n+1) end:
q:= n-> isprime(n) and andmap(t, [n-prevprime(n), nextprime(n)-n]):
select(q, [$3..5000])[];
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MATHEMATICA
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t[n_] := IntegerQ@Sqrt[8n+1];
q[n_] := PrimeQ[n] && t[n-NextPrime[n, -1]] && t[NextPrime[n]-n];
Select[Range[3, 5000], q] (* Jean-François Alcover, May 14 2022, after Alois P. Heinz *)
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CROSSREFS
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Cf. A000040, A000217, A014494, A353088, A353135, A353137.
Sequence in context: A044766 A342450 A160058 * A053070 A140655 A142508
Adjacent sequences: A353133 A353134 A353135 * A353137 A353138 A353139
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Apr 25 2022
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STATUS
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approved
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