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A320703
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Indices of primes followed by a gap (distance to next larger prime) of 10.
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6
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34, 42, 53, 61, 68, 80, 82, 101, 106, 115, 125, 127, 138, 141, 145, 157, 172, 175, 177, 191, 193, 204, 222, 233, 258, 266, 269, 279, 289, 306, 308, 310, 316, 324, 369, 383, 397, 399, 403, 418, 422, 431, 443, 474, 491, 497, 500, 502, 518, 525, 531, 535, 575
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OFFSET
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1,1
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COMMENTS
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Indices of the primes given in A031928.
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LINKS
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FORMULA
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A320703 = { i > 0 | prime(i+1) = prime(i) + 10 }.
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MATHEMATICA
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Select[Range[1000], Prime[#] + 10 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 21 2019 *)
Position[Partition[Prime[Range[600]], 2, 1], _?(#[[2]]-#[[1]]==10&), 1, Heads-> False]//Flatten (* Harvey P. Dale, Mar 08 2020 *)
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PROG
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(PARI) A320703_vec(N=100, g=10, p=2, i=primepi(p)-1, L=List())={forprime(q=1+p, , i++; if(p+g==p=q, listput(L, i); N--||break)); Vec(L)} \\ returns the list of first N terms of the sequence
(Magma) [n: n in [1..1000] | NthPrime(n+1) - NthPrime(n) eq 10]; // Vincenzo Librandi, Mar 21 2019
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CROSSREFS
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Subsequence of A107730: prime(n+1) ends in same digit as prime(n).
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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