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A331031 The prime numbers that are prime-indexed primes and whose digit sum, adjacent digit sum concatenation, and adjacent digit difference concatenation are also primes. 2
41, 83, 401, 2063, 6863, 10909, 20063, 26489, 44621, 105229, 187067, 205507, 233267, 238547, 240047, 243301, 256307, 346763, 367021, 376003, 395581, 555707, 562181, 563467, 600203, 613243, 644843, 675263, 689789, 785801, 787601, 837667, 845381, 954263, 959389, 1070203 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence lists the prime numbers that are prime-indexed primes, see A006450, and whose digit sum A007953, concatenation of adjacent digit sums A053392, and concatenation of adjacent digit differences A040115, are also primes. This is a subsequence of A006450 and A330653. There are 267 terms for primes up to 20491057.
LINKS
Wikipedia, Super prime.
EXAMPLE
a(4) = 2063 as 2063 is the 311th prime, 2+0+6+3 = 11, '2+0'+'0+6'+'6+3' = 269, '|2-0|'+'|0-6|'+'|6-3|' = 263, and 2063, 311, 11, 269, 263 are all prime.
CROSSREFS
Sequence in context: A141898 A054998 A067378 * A171138 A071886 A276302
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Jan 07 2020
STATUS
approved

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Last modified February 27 04:33 EST 2024. Contains 370362 sequences. (Running on oeis4.)